JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Current Electricity

In the given figure switches

S_{1}

and

S_{2}

are in open condition. The resistance across ab when the switches

S_{1}

and

S_{2}

are closed is ____

Ω

Answer: 10

Solution

Closing

S_{1}

joins the junction between the

12 Ω

and

4 Ω

resistors of the upper arm to the junction between the

6 Ω

and

4 Ω

resistors of the lower arm, and closing

S_{2}

joins the two remaining junctions. The network between

a

and

b

then reduces to three parallel pairs in series:

R_{ab} = \frac{12 \times 6}{12 + 6} + \frac{4 \times 4}{4 + 4} + \frac{6 \times 12}{6 + 12} = 4 + 2 + 4

The resistance across

ab

10 Ω

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Integer answer