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]

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(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]

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(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]

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(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

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

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

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]

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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]

0%

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

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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]

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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]

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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]

0%

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

0%

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]

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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]