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

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]

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(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]

[IMAGE 177]

$I_{4} = \frac{8}{5} A$ 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]

[IMAGE 178]

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

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(1)

[IMAGE 179]

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

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

$\Rightarrow R_{eq} = \frac{2}{3} Ω$

Q 16 :

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

[IMAGE 180]

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

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(4)

Wheatstone bridge is in balanced condition.

[IMAGE 181]

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

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)

[IMAGE 182]

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

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

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

Q 18 :

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

[IMAGE 183]

$5 k Ω$
$20 k Ω$
$10 k Ω$
$30 k Ω$

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(1)

[IMAGE 184]

$All resistors are in parallel.$

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

$R_{eq} = 5 k Ω$

Q 19 :

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

[IMAGE 185]

$24 Ω$
$3.2 Ω$
$20 Ω$
$16 Ω$

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(2)

The circuit can be reduced to

[IMAGE 186]

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

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)

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

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

Topic Question Set

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]

0%

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]

[IMAGE 177]

Q 15 :

The equivalent resistance between A and B is [2023]

[IMAGE 178]

Q 16 :

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

[IMAGE 180]

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]

[IMAGE 183]

Q 19 :

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

[IMAGE 185]

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Topic Question Set

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Q 15 : The equivalent resistance between A and B is [2023] [IMAGE 178] .question-row { display: flex; align-items: flex-start; gap: 8px; } .q-no { font-size: 17px; white-space: nowrap; margin-left: -15px; } .q-text { font-size: 18px; flex: 1; } .q-no, .q-text p { line-height: 30px; }

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Q 15 :

The equivalent resistance between A and B is [2023]

[IMAGE 178]