The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_{1}$ to $R_{8}$, and two ideal batteries with voltages $\varepsilon_{1}=12 V$ and $\varepsilon_{2}=6 V$. Which of the following statement(s) is(are) correct?

(A) The magnitude of current flowing through $R_{1}$ is $7.2 A$.; (B) The magnitude of current flowing through $R_{2}$ is $1.2 A$.; (C) The magnitude of current flowing through $R_{3}$ is $4.8 A$.; (D) The magnitude of current flowing through $R_{5}$ is $2.4 A$.

JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Current Electricity

WhatsApp Email

The figure shows a circuit having eight resistances of

1Ω

each, labelled

R_{1}

R_{8}

, and two ideal batteries with voltages

ε_{1} = 12 V

and

ε_{2} = 6 V

.

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

(A)The magnitude of current flowing through $R_{1}$ is $7.2 A$ .✓ Correct
(B)The magnitude of current flowing through $R_{2}$ is $1.2 A$ .✓ Correct
(C)The magnitude of current flowing through $R_{3}$ is $4.8 A$ .✓ Correct
(D)The magnitude of current flowing through $R_{5}$ is $2.4 A$ .✓ Correct

Answer: (A), (B), (C), (D)

Solution

Using Kirchhoff's laws and nodal analysis:

At the central node with potential

V_{0}

\frac{18 - V _{0}}{3/2} + \frac{12 - V _{0}}{1/2} + \frac{0 - V _{0}}{3/2} = 0

Solving:

V_{0} = \frac{54}{5}

V

For another node at potential

V^{'}

\frac{2 ( 54/5 - V ^{'} )}{1} + \frac{18 - V ^{'}}{1} = 0

Solving:

V^{'} = \frac{66}{5}

V

Current calculations:

$I_{R_{1}} = \frac{36}{5} = 7.2$ A
$I_{R_{2}} = \frac{6}{5} = 1.2$ A
$I_{R_{3}} = \frac{24}{5} = 4.8$ A
$I_{R_{5}} = \frac{12}{5} = 2.4$ A

All four statements are correct.

JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · One or more correct options

Practise more: all JEE Advanced PYQs on Current Electricity →

JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Current Electricity

Solution

More JEE Advanced questions on Current Electricity