Electric Resistance and Simple Circuits | Physics JEE previous year questions with Solutions

Q 1 :

A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be [2024]

1/25 R
1/5 R
25 R
5 R

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(1)

Resistance of each part = $\frac{R}{5}$

Total resistance = $\frac{1}{5} \times \frac{R}{5} = \frac{R}{25}$

Q 2 :

In the given figure $R_{1} = 10 Ω, R_{2} = 8 Ω, R_{3} = 4 Ω$ and $R_{4} = 8 Ω .$ Battery is ideal with emf 12 V. Equivalent resistance of the circuit and current supplied by battery are respectively [2024]

$10.5 Ω and 1.14 A$
$12 Ω and 1 A$
$10.5 Ω and 1 A$
$12 Ω and 11.4 A$

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(2)

Here $R_{2}, R_{3}, R_{4}$ are in parallel,

$\frac{1}{R_{234}} = \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}} \Rightarrow R_{234}$

$R_{234}$ is in series with $R_{1}$ , so

Equivalent resistant, $R_{eq} = R_{234} + R_{1} = 2 + 10 = 12 Ω$

The current supplied by the battery, $i = \frac{12}{12} = 1 A$

Q 3 :

The equivalent resistance between A and B is: [2024]

$18 Ω$
$25 Ω$
$27 Ω$
$19 Ω$

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(4)

$R_{eq} = 5 Ω + 6 Ω + 8 Ω = 19 Ω$

Q 4 :

The effective resistance between A and B, if resistance of each resistor is R, will be [2024]

$\frac{2}{3} R$
$\frac{8 R}{3}$
$\frac{5 R}{3}$
$\frac{4 R}{3}$

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(2)

From symmetry we can remove two middle resistances. New circuit is

Q 5 :

Twelve wires each having resistance $2 Ω$ are joined to form a cube. A battery of $6 V$ emf is joined across points $a$ and $c$ . The voltage difference between $e$ and $f$ is ____ $V$ . [2024]

(1)

$∴$ $R_{eq} = \frac{R \times 3 R}{R + 3 R} = \frac{3}{4} R \Rightarrow R_{eq} = \frac{3}{4} \times 2 = \frac{3}{2} Ω$

$∴$ Current through battery $= \frac{6 \times 2}{3} = 4 A$

The current through $a - h, i_{a h} = \frac{4}{8} \times 2 = 1 A$

$∴$ $∆ V$ across $e - f = \frac{i_{a h}}{2} \times R = \frac{1}{2} \times 2 = 1 V$

Q 6 :

A wire of resistance 20 $Ω$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ____ $Ω$ . [2024]

(5)

Resistance of each part $R = \frac{20}{10} = 2 Ω$

2 parts are connected in parallel $R' = \frac{2}{2} = 1 Ω$

Now, there will be 5 parts, each of resistance $1 Ω$ , they are connected in series.

$R_{eq} = 5 R' \Rightarrow R_{eq} = 5 Ω$

Q 7 :

Equivalent resistance of the following network is _______ $Ω$ . [2024]

(1)

$R_{eq} = 3 \times \frac{1}{3} = 1 Ω$

Q 8 :

Find the equivalent resistance between two ends of the following circuit. [2025]

r
$\frac{r}{6}$
$\frac{r}{9}$
$\frac{r}{3}$

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(3)

$\Rightarrow \frac{1}{R_{eq}} = \frac{1}{\frac{r}{3}} + \frac{1}{\frac{r}{3}} + \frac{1}{\frac{r}{3}}$

Or $R_{eq} = \frac{r}{9}$

Q 9 :

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is [2025]

9/8
8/9
27/32
32/27

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(4)

For the wire bent into an equilateral triangle, each side has a resistance $\frac{R}{3}$

$R_{eq} = \frac{(\frac{2 R}{3}) (\frac{R}{3})}{\frac{2 R}{3} + \frac{R}{3}} = \frac{2 R}{9} = R_{1}$ (lets say)

.For the wire bent into a square, each side has a resistance $\frac{R}{4}$

. $R_{eq} = \frac{(\frac{3 R}{4}) (\frac{R}{4})}{\frac{3 R}{4} + \frac{R}{4}} = \frac{3 R}{16} = R_{3}$ (lets say)

$\Rightarrow \frac{R_{1}}{R_{3}} = \frac{\frac{2 R}{9}}{\frac{3 R}{16}} = \frac{32}{27}$

Q 10 :

A wire of length 25 m and cross-sectional area 5 ${mm}^{2}$ having resistivity of $2 \times 10^{- 6} Ωm$ is bent into a complete circle. The resistance between diametrically opposite points will be [2025]

12.5 $Ω$
50 $Ω$
100 $Ω$
25 $Ω$

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(none)

Let R be total resistance across ends of wire, then

$R = \frac{ρ L}{A} = \frac{2 \times 10^{- 6} \times 25}{5 \times 10^{- 6}} = 10 Ω$

$R_{eq} = \frac{R}{4} = \frac{10}{4} = 2.5 Ω$

Q 11 :

From the combination of resistors with resistance values $R_{1} = R_{2} = R_{3} = 5 Ω$ and $R_{4} = 10 Ω$ , which of the following combination is the best circuit to get an equivalent resistance of $6 Ω$ ? [2025]

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(1)

$\frac{1}{R_{eq}} = \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{1}{6} \Rightarrow R_{e q} = 6 Ω$

Q 12 :

A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is $R / n$ . The value of n is: [2025]

16
14
10
12

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(4)

As, $r = \frac{R}{6}$

(As balanced wheat stone bridge is formed)

Now, Equivalent resistance between A and B can be written as

Clearly, $R_{1} = \frac{r}{6}$

So, $R_{A B} = R_{1} ∥ 2 R_{1} ∥ 2 R_{1}$

$\Rightarrow \frac{1}{R_{A B}} = \frac{1}{R_{1}} + \frac{1}{2 R_{1}} + \frac{1}{2 R_{1}} = \frac{4}{2 R_{1}} = \frac{2}{R_{1}}$

$\Rightarrow R_{A B} = \frac{R_{1}}{2} = \frac{r}{12}$

Q 13 :

A wire of resistance 9 $Ω$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be ____ ohm. [2025]

(2)

9 $Ω$ is the resistance of whole wire

$∴$ Resistance of each wire = 3 $Ω$

$∴$ Equivalent resistance = 2 $Ω$

Q 14 :

As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of $3 Ω$ . The currents through the resistors $R_{4}$ and $R_{5}$ are $I_{4}$ and $I_{5}$ respectively. The values of $I_{4}$ and $I_{5}$ are [2023]

$I_{4} = \frac{8}{5} A$ and $I_{5} = \frac{2}{5} A$
$I_{4} = \frac{6}{5} A$ and $I_{5} = \frac{24}{5} A$
$I_{4} = \frac{2}{5} A$ and $I_{5} = \frac{8}{5} A$
$I_{4} = \frac{24}{5} A$ and $I_{5} = \frac{6}{5} A$

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(3)

$Equivalent resistance of circuit$

$R_{eq} = 3 + 1 + 2 + 4 + 2 = 12 Ω$

$Current through battery i = \frac{24}{12} = 2 A$

$I_{4} = \frac{R_{5}}{R_{4} + R_{5}} \times 2 = \frac{5}{20 + 5} \times 2 = \frac{2}{5} A$

$I_{5} = 2 - \frac{2}{5} = \frac{8}{5} A$

Q 15 :

The equivalent resistance between A and B is [2023]

$\frac{2}{3} Ω$
$\frac{1}{2} Ω$
$\frac{3}{2} Ω$
$\frac{1}{3} Ω$

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(1)

$\frac{1}{R_{eq}} = \frac{1}{2} + \frac{1}{12} + \frac{1}{4} + \frac{1}{6} + \frac{1}{2}$

$= \frac{6 + 1 + 3 + 2 + 6}{12} = \frac{18}{12} = \frac{3}{2}$

$\Rightarrow R_{eq} = \frac{2}{3} Ω$

Q 16 :

The equivalent resistance between A and B of the network shown in the figure: [2023]

$11 \frac{2 R}{3}$
$14 R$
$21 R$
$\frac{8}{3} R$

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(4)

Wheatstone bridge is in balanced condition.

$\frac{1}{R_{eq}} = \frac{1}{4 R} + \frac{1}{8 R} \Rightarrow R_{eq} = \frac{8 R}{3}$

Q 17 :

Equivalent resistance between the adjacent corners of a regular $n$ -sided polygon of uniform wire of resistance $R$ would be [2023]

$\frac{(n - 1) R}{n^{2}}$
$\frac{(n - 1) R}{(2 n - 1)}$
$\frac{n^{2} R}{(n - 1)}$
$\frac{(n - 1) R}{n}$

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(1)

$Suppose resistance of each arm is r, then r = \frac{R}{n}$

$R_{eq} (A B) = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$

$= \frac{r (n - 1) r}{r + (n - 1) r} = \frac{r (n - 1) r}{n r} = \frac{n - 1}{n} r = \frac{(n - 1) R}{n^{2}}$

Q 18 :

The equivalent resistance between A and B as shown in the figure is [2023]

$5 k Ω$
$20 k Ω$
$10 k Ω$
$30 k Ω$

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(1)

$All resistors are in parallel.$

$So, \frac{1}{R_{eq}} = \frac{1}{10} + \frac{1}{20} + \frac{1}{20}$

$R_{eq} = 5 k Ω$

Q 19 :

The equivalent resistance of the circuit shown below between points $a$ and $b$ is [2023]

$24 Ω$
$3.2 Ω$
$20 Ω$
$16 Ω$

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(2)

The circuit can be reduced to

$\Rightarrow R_{eq} = \frac{16 \times 4}{16 + 4} = \frac{16}{5} Ω = 3.2 Ω$

Q 20 :

Given below are two statements: [2023]

Statement I: The equivalent resistance of resistors in a series combination is smaller than the least resistance used in the combination.

Statement II: The resistivity of the material is independent of temperature.

In the light of the above statements, choose the correct answer from the options given below:

Statement I is false but Statement II is true
Both Statement I and Statement II are false
Statement I is true but Statement II is false
Both Statement I and Statement II are true

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(2)

$R_{eq} = R_{1} + R_{2} + R_{3} \Rightarrow St-1 False$

$Resistivity depends on temperature. \Rightarrow St-2 False$

Q 21 :

In the given circuit, the current $(I)$ through the battery will be [2023]

1.5 A
1 A
2.5 A
2 A

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(1)

$In the circuit D_{1} and D_{3} are forward biased and D_{2} is reverse biased.$

$∴$ $I = \frac{10}{20 / 3} = \frac{10 \times 3}{20} = \frac{3}{2} A = 1.5 A$

Q 22 :

In the given circuit, the equivalent resistance between the terminal A and B is ________ $Ω$ . [2023]

(10)

$R_{A B} = 3 + 1 + 6 = 10 Ω$

Q 23 :

If the potential difference between $B$ and $D$ is zero, the value of $x$ is $\frac{1}{n} Ω$ . The value of $n$ is ______. [2023]

(2)

$\frac{2}{3} = \frac{\frac{x}{x + 1}}{x}$

$\Rightarrow \frac{2}{3} = \frac{1}{x + 1}$

$\Rightarrow x = 0.5 = \frac{1}{2}$

$\Rightarrow n = 2$

Q 24 :

10 resistors each of resistance 10 $Ω$ can be connected in such a way as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ________. [2023]

(100)

Maximum resistance occurs

When all the resistors are connected in series combination

$∴$ $R_{\max} = 10 R$

$Here R = 10 Ω$

Minimum resistance occurs

When all the resistances are connected in parallel combination

$R_{\min} = \frac{R}{10}$

$∴$ $\frac{R_{\max}}{R_{\min}} = 100$

Q 25 :

A wire of uniform resistance $λ Ω / m$ is bent into a circle of radius $r$ and another piece of wire with length $2 r$ is connected between points A and B (AOB) as shown in the figure. The equivalent resistance between points A and B is _______ $Ω$ . [2026]

$2 π λ r$
$\frac{3 π λ r}{8}$
$\frac{6 π λ r}{3 π + 16}$
$(π + 1) 2 r λ$

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(3)

$\frac{1}{R_{A B}} = \frac{2}{λ π r} + \frac{1}{λ \cdot 2 r} + \frac{2}{λ \cdot 3 π r}$

$= \frac{1}{λ r} [\frac{2}{π} + \frac{1}{2} + \frac{2}{3 π}]$

$= \frac{1}{λ r} (\frac{12 + 3 π + 4}{6 π}) = \frac{1}{λ r} (\frac{16 + 3 π}{6 π})$

$R_{A B} = λ r (\frac{6 π}{16 + 3 π})$

Q 26 :

A regular hexagon is formed by six wires each of resistance $r Ω$ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be [2026]

$\frac{3}{4} r$
$\frac{4}{5} r$
$\frac{5}{8} r$
$\frac{3}{5} r$

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(2)

$R_{eq} = \frac{2 R \times \frac{4 R}{3}}{2 R + \frac{4 R}{3}} = \frac{8 R^{2}}{10 R} = \frac{4}{5} R$

Q 27 :

Two known resistances of $R Ω and 2 R Ω$ and one unknown resistance $X Ω$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $X Ω$ then the value of X is ______ $Ω .$ [2026]

$(\sqrt{3} - 1) R$
$2 (\sqrt{3} - 1) R$
R
$(\sqrt{3} + 1) R$

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(1)

$\frac{(2 R + x) (R)}{3 R + x} = x$

$x^{2} + 2 R x - 2 R^{2} = 0$

$x = (\sqrt{3} - 1) R$

Q 28 :

The equivalent resistance between the points A and B in the following circuit is $\frac{x}{5} Ω$ . The value of $x$ is __________. [2026]

(21)

$6 i_{1} + 3 (2 i_{1} - i) = 3 (i - i_{1})$

$\Rightarrow 15 i_{1} = 6 i \Rightarrow i_{1} = \frac{2}{5} i . . . (1)$

$3 (i - i_{1}) + 6 i_{1} = 1$

$3 i + 3 i_{1} = 1$

$(3 + \frac{6}{5}) i = 1$

$\Rightarrow i = \frac{5}{21} A = \frac{1 V}{R_{eq}} \Rightarrow R_{eq} = \frac{21}{5} Ω$

Topic Question Set

Q 1 :

A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be [2024]

Q 2 :

In the given figure $R_{1} = 10 Ω, R_{2} = 8 Ω, R_{3} = 4 Ω$ and $R_{4} = 8 Ω .$ Battery is ideal with emf 12 V. Equivalent resistance of the circuit and current supplied by battery are respectively [2024]

Q 3 :

The equivalent resistance between A and B is: [2024]

Q 4 :

The effective resistance between A and B, if resistance of each resistor is R, will be [2024]

Q 5 :

Twelve wires each having resistance $2 Ω$ are joined to form a cube. A battery of $6 V$ emf is joined across points $a$ and $c$ . The voltage difference between $e$ and $f$ is ____ $V$ . [2024]

Q 6 :

A wire of resistance 20 $Ω$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ____ $Ω$ . [2024]

Q 7 :

Equivalent resistance of the following network is _______ $Ω$ . [2024]

Q 8 :

Find the equivalent resistance between two ends of the following circuit. [2025]

Q 9 :

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is [2025]

Q 10 :

A wire of length 25 m and cross-sectional area 5 ${mm}^{2}$ having resistivity of $2 \times 10^{- 6} Ωm$ is bent into a complete circle. The resistance between diametrically opposite points will be [2025]

Q 11 :

From the combination of resistors with resistance values $R_{1} = R_{2} = R_{3} = 5 Ω$ and $R_{4} = 10 Ω$ , which of the following combination is the best circuit to get an equivalent resistance of $6 Ω$ ? [2025]

Q 12 :

A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is $R / n$ . The value of n is: [2025]

Q 13 :

A wire of resistance 9 $Ω$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be ____ ohm. [2025]

Q 14 :

As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of $3 Ω$ . The currents through the resistors $R_{4}$ and $R_{5}$ are $I_{4}$ and $I_{5}$ respectively. The values of $I_{4}$ and $I_{5}$ are [2023]

Q 15 :

The equivalent resistance between A and B is [2023]

Q 16 :

The equivalent resistance between A and B of the network shown in the figure: [2023]

Q 17 :

Equivalent resistance between the adjacent corners of a regular $n$ -sided polygon of uniform wire of resistance $R$ would be [2023]

Q 18 :

The equivalent resistance between A and B as shown in the figure is [2023]

Q 19 :

The equivalent resistance of the circuit shown below between points $a$ and $b$ is [2023]

Q 21 :

In the given circuit, the current $(I)$ through the battery will be [2023]

Q 22 :

In the given circuit, the equivalent resistance between the terminal A and B is ________ $Ω$ . [2023]

Q 23 :

If the potential difference between $B$ and $D$ is zero, the value of $x$ is $\frac{1}{n} Ω$ . The value of $n$ is ______. [2023]

Q 24 :

10 resistors each of resistance 10 $Ω$ can be connected in such a way as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ________. [2023]

Q 25 :

A wire of uniform resistance $λ Ω / m$ is bent into a circle of radius $r$ and another piece of wire with length $2 r$ is connected between points A and B (AOB) as shown in the figure. The equivalent resistance between points A and B is _______ $Ω$ . [2026]

Q 27 :

Two known resistances of $R Ω and 2 R Ω$ and one unknown resistance $X Ω$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $X Ω$ then the value of X is ______ $Ω .$ [2026]

Q 28 :

The equivalent resistance between the points A and B in the following circuit is $\frac{x}{5} Ω$ . The value of $x$ is __________. [2026]

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Topic Question Set

Q 1 : A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be [2024]

Q 2 : In the given figure R1=10Ω,R2=8Ω,R3=4Ω and R4=8Ω. Battery is ideal with emf 12 V. Equivalent resistance of the circuit and current supplied by battery are respectively [2024]

Q 3 : The equivalent resistance between A and B is: [2024]

Q 4 : The effective resistance between A and B, if resistance of each resistor is R, will be [2024]

Q 5 : Twelve wires each having resistance 2Ω are joined to form a cube. A battery of 6V emf is joined across points a and c. The voltage difference between e and f is ____ V. [2024]

Q 6 : A wire of resistance 20 Ω is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ____ Ω. [2024]

Q 7 : Equivalent resistance of the following network is _______ Ω. [2024]

Q 8 : Find the equivalent resistance between two ends of the following circuit. [2025]

Q 9 : A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is [2025]

Q 10 : A wire of length 25 m and cross-sectional area 5 mm2 having resistivity of 2×10–6Ωm is bent into a complete circle. The resistance between diametrically opposite points will be [2025]

Q 11 : From the combination of resistors with resistance values R1=R2=R3=5Ω and R4=10Ω, which of the following combination is the best circuit to get an equivalent resistance of 6Ω? [2025]

Q 12 : A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is: [2025]

Q 13 : A wire of resistance 9Ω is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be ____ ohm. [2025]

Q 14 : As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3 Ω. The currents through the resistors R4 and R5 are I4 and I5 respectively. The values of I4 and I5 are [2023]

Q 15 : The equivalent resistance between A and B is [2023]

Q 16 : The equivalent resistance between A and B of the network shown in the figure: [2023]

Q 17 : Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be [2023]

Q 18 : The equivalent resistance between A and B as shown in the figure is [2023]

Q 19 : The equivalent resistance of the circuit shown below between points a and b is [2023]

Q 21 : In the given circuit, the current (I) through the battery will be [2023]

Q 22 : In the given circuit, the equivalent resistance between the terminal A and B is ________ Ω. [2023]

Q 23 : If the potential difference between B and D is zero, the value of x is 1nΩ. The value of n is ______. [2023]

Q 24 : 10 resistors each of resistance 10Ω can be connected in such a way as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ________. [2023]

Q 25 : A wire of uniform resistance λ Ω/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (AOB) as shown in the figure. The equivalent resistance between points A and B is _______ Ω. [2026]

Q 27 : Two known resistances of RΩ and 2RΩ and one unknown resistance XΩ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is XΩ then the value of X is ______Ω. [2026]

Q 28 : The equivalent resistance between the points A and B in the following circuit is x5Ω. The value of x is __________. [2026]

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Q 1 :

A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be [2024]

Q 2 :

In the given figure $R_{1} = 10 Ω, R_{2} = 8 Ω, R_{3} = 4 Ω$ and $R_{4} = 8 Ω .$ Battery is ideal with emf 12 V. Equivalent resistance of the circuit and current supplied by battery are respectively [2024]

Q 3 :

The equivalent resistance between A and B is: [2024]

Q 4 :

The effective resistance between A and B, if resistance of each resistor is R, will be [2024]

Q 5 :

Twelve wires each having resistance $2 Ω$ are joined to form a cube. A battery of $6 V$ emf is joined across points $a$ and $c$ . The voltage difference between $e$ and $f$ is ____ $V$ . [2024]

Q 6 :

A wire of resistance 20 $Ω$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ____ $Ω$ . [2024]

Q 7 :

Equivalent resistance of the following network is _______ $Ω$ . [2024]

Q 8 :

Find the equivalent resistance between two ends of the following circuit. [2025]

Q 9 :

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is [2025]

Q 10 :

A wire of length 25 m and cross-sectional area 5 ${mm}^{2}$ having resistivity of $2 \times 10^{- 6} Ωm$ is bent into a complete circle. The resistance between diametrically opposite points will be [2025]

Q 11 :

From the combination of resistors with resistance values $R_{1} = R_{2} = R_{3} = 5 Ω$ and $R_{4} = 10 Ω$ , which of the following combination is the best circuit to get an equivalent resistance of $6 Ω$ ? [2025]

Q 12 :

A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is $R / n$ . The value of n is: [2025]

Q 13 :

A wire of resistance 9 $Ω$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be ____ ohm. [2025]

Q 14 :

As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of $3 Ω$ . The currents through the resistors $R_{4}$ and $R_{5}$ are $I_{4}$ and $I_{5}$ respectively. The values of $I_{4}$ and $I_{5}$ are [2023]

Q 15 :

The equivalent resistance between A and B is [2023]

Q 16 :

The equivalent resistance between A and B of the network shown in the figure: [2023]

Q 17 :

Equivalent resistance between the adjacent corners of a regular $n$ -sided polygon of uniform wire of resistance $R$ would be [2023]

Q 18 :

The equivalent resistance between A and B as shown in the figure is [2023]

Q 19 :

The equivalent resistance of the circuit shown below between points $a$ and $b$ is [2023]

Q 21 :

In the given circuit, the current $(I)$ through the battery will be [2023]

Q 22 :

In the given circuit, the equivalent resistance between the terminal A and B is ________ $Ω$ . [2023]

Q 23 :

If the potential difference between $B$ and $D$ is zero, the value of $x$ is $\frac{1}{n} Ω$ . The value of $n$ is ______. [2023]

Q 24 :

10 resistors each of resistance 10 $Ω$ can be connected in such a way as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ________. [2023]

Q 25 :

A wire of uniform resistance $λ Ω / m$ is bent into a circle of radius $r$ and another piece of wire with length $2 r$ is connected between points A and B (AOB) as shown in the figure. The equivalent resistance between points A and B is _______ $Ω$ . [2026]

Q 27 :

Two known resistances of $R Ω and 2 R Ω$ and one unknown resistance $X Ω$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $X Ω$ then the value of X is ______ $Ω .$ [2026]

Q 28 :

The equivalent resistance between the points A and B in the following circuit is $\frac{x}{5} Ω$ . The value of $x$ is __________. [2026]