A Wheatstone bridge is balanced. Find the rat | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In a balanced Wheatstone bridge,the potential difference across the bridge is the same for both branches if connected in parallel. However,the sta

Vedclass · Accepted Answer

$R : P$

Vedclass · Answer

(B) In a balanced Wheatstone bridge,the potential difference across the bridge is the same for both branches if connected in parallel. However,the standard configuration shows the branches $(P, Q)$ and $(R, S)$ are in series with each other in parallel arms. Let the total voltage across the parallel branches be $V$. The power dissipated in a resistor is given by $P_{diss} = \frac{V^2}{R_{eq}}$. For the branch $(P+Q)$,the power is $P_1 = \frac{V^2}{P+Q}$. For the branch $(R+S)$,the power is $P_2 = \frac{V^2}{R+S}$. The ratio is $\frac{P_1}{P_2} = \frac{V^2/(P+Q)}{V^2/(R+S)} = \frac{R+S}{P+Q}$. Since the bridge is balanced,$\frac{P}{R} = \frac{Q}{S}$,which implies $PS = QR$,or $\frac{S}{Q} = \frac{R}{P}$. Also,from the balanced condition $\frac{P}{Q} = \frac{R}{S}$,we can write $S = \frac{RQ}{P}$. Substituting $S$ into the ratio: $\frac{R + RQ/P}{P + Q} = \frac{R(1 + Q/P)}{P + Q} = \frac{R(P+Q)/P}{P+Q} = \frac{R}{P}$. Thus,the ratio is $R:P$.

$A$ Wheatstone bridge is balanced. Find the ratio of electric power dissipated in $(P + Q)$ to $(R + S)$.

Similar Questions

If $\frac{3x + 4}{x^2 - 3x + 2} = \frac{A}{x - 2} - \frac{B}{x - 1}$,then $(A, B) = $

$A$ radioactive nucleus (initial mass number $A$ and atomic number $Z$) emits $3 \,\alpha-$ particles and $2$ positrons. The ratio of the number of neutrons to that of protons in the final nucleus will be:

The value of the series $x \log _e a + \frac{x^3}{3!} (\log _e a)^3 + \frac{x^5}{5!} (\log _e a)^5 + \dots$ is

$A$ proton, a deuteron (nucleus of ${ }_1 H^2$) and an $\alpha$-particle with the same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module