In a Wheatstone bridge (see figure) Resistance $P$ and $Q$ are approximately equal. When $\mathrm{R}=400 \Omega$, the bridge is balanced. On interchanging P and Q , the value of R , for balance is $405 \Omega$. The value of X is close to:

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Current Electricity

In a Wheatstone bridge (see figure) Resistance

P

and

Q

are approximately equal. When

R = 400Ω

, the bridge is balanced. On interchanging P and Q , the value of R , for balance is

405Ω

. The value of X is close to:

Answer: (D)

At balance

\frac{P}{Q} = \frac{R}{X}

, so

\frac{P}{Q} = \frac{400}{X}

. Interchanging

P

and

Q

and rebalancing gives

\frac{Q}{P} = \frac{405}{X}

. Multiplying the two relations the ratio

P / Q

cancels and

1 = \frac{400 \times 405}{X ^{2}}

, so

X = 400 \times 405 \approx 402.5 Ω

. The unknown resistance is the geometric mean of the two balancing values.

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option