Physics · Current Electricity

JEE Advanced 2022 — Paper 1 — Question 28

The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $\mathrm{R}_{1}$ to $\mathrm{R}_{8}$ ,

and two ideal batteries with voltages $\varepsilon_{1}=12 \mathrm{~V}$ and $\varepsilon_{2}=6 \mathrm{~V}$ .

Which of the following statement(s) is(are) correct?

Option A:
The magnitude of current flowing through $\mathrm{R}_{1}$ is 7.2 A .
Correct
Option B:
The magnitude of current flowing through $R_{2}$ is 1.2 A .
Correct
Option C:
The magnitude of current flowing through $R_{3}$ is 4.8 A .
Correct
Option D:
The magnitude of current flowing through $\mathrm{R}_{5}$ is 2.4 A .
Correct

Answer: A, B, C, D

$-\left(i-i_{1}\right)+6-\frac{1}{2}\left(i-i_{1}\right)+\frac{1}{2} i_{1}=0$

$-\frac{3}{2}\left(i-i_{1}\right)+\frac{i_{1}}{2}+6=0$

$-\frac{3}{2} \mathrm{i}+\frac{3}{2} \mathrm{i}_{1}+\frac{\mathrm{i}_{2}}{2}+6=0$

$-\frac{3}{2} \mathrm{i}+2 \mathrm{i}_{1}+6=0$

$-\frac{i_{1}}{2}-\frac{i}{2}-i+12=0$ $-\frac{\mathrm{i}_{1}}{2}-\frac{3}{2} \mathrm{i}+12=0$

$\frac{5}{2} \mathrm{i}_{1}-6=0$ $\mathrm{i}_{1}=\frac{6 \times 2}{5}=\frac{12}{5}=2.4$

$-1.2-1.5 \mathrm{i}+12=0$ $1.5 \mathrm{i}=10.8$ $i=\frac{10.8}{1.5}$ 0

$\mathrm{i}=7.2$

Answer key and solution verified before publishing.

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