In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R = 400 Ω, the bridge is equal. When R = 400 Ω, the bridge is balanced. On inter-changing P and Q, the value of R, for balance, is 405 Ω . The value of X is close to :

Question

In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R = 400 Ω, the bridge is equal. When R = 400 Ω, the bridge is balanced. On inter-changing P and Q, the value of R, for balance, is 405 Ω . The value of X is close to : (A) 403.5 ohm (B) 404.5 ohm (C) 401.5 ohm (D) 402.5 ohm

Tardigrade Admin · Accepted Answer

Initiality ( P / Q )=( R 1/ X ) After interchanging P and Q ( Q / P )=( R 2/ X ) From (1) and (2) 1=( R 1 × R 2/ X 2) X =√ R 1 R 2 X =√400 × 405=402.5 Ω

Q. In a Wheatstone bridge (see fig.), Resistances $P$ and $Q$ are approximately equal. When $R = 400 Ω$ , the bridge is equal. When $R = 400 Ω$ , the bridge is balanced. On inter-changing $P$ and $Q$ , the value of $R$ , for balance, is $405 Ω$ .
The value of $X$ is close to :

403.5 ohm

404.5 ohm

401.5 ohm

402.5 ohm

Initiality
$\frac{P}{Q} = \frac{R _{1}}{X}$
After interchanging $P$ and $Q$
$\frac{Q}{P} = \frac{R _{2}}{X}$
From (1) and (2)
$1 = \frac{R _{1} \times R _{2}}{X ^{2}}$
$X = R_{1} R_{2}$
$X = 400 \times 405 = 402.5Ω$

Q. In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R=400Ω, the bridge is equal. When R=400Ω, the bridge is balanced. On inter-changing P and Q, the value of R, for balance, is 405Ω . The value of X is close to :