In the given circuit, the current flowing through the resistance $20 \Omega$ is 0.3 A , while the ammeter reads 0.9 A . The value of $\mathrm{R}_{1}$ is ______ $\Omega$.

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Current Electricity

In the given circuit, the current flowing through the resistance

20Ω

is 0.3 A , while the ammeter reads 0.9 A . The value of

R_{1}

is ______

Ω

Answer: 30

Let

i_{1}, i_{2}, i_{3}

be the currents through the 20 Ω, 15 Ω and

R_{1}

branches, all connected in parallel between the same two nodes A and B. Given

i_{1} = 0.3

A and

i_{1} + i_{2} + i_{3} = 0.9

A (the ammeter reading).

The voltage across every parallel branch is the same:

V_{A B} = i_{1} \times 20 = 0.3 \times 20 = 6 V

Current through the 15 Ω branch:

i_{2} = \frac{6}{15} = 0.4 A

From the total current:

i_{3} = 0.9 - 0.3 - 0.4 = 0.2 A

Applying Ohm's law to the

R_{1}

branch:

R_{1} = \frac{V _{A B}}{i _{3}} = \frac{6}{0.2} = 30 Ω

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Integer answer