Question

The circuit shown below is a deflection bridge. the variable resistor, r3, has been adjusted so that its resistance is 132 ω such that the deflection bridge is in the balanced state with: vs = 10 v r1 = 33 ω r2 = 48 ω r4 = 192 ω

A) 0.15 A
B) 0.20 A
C) 0.25 A
D) 0.30 A

Answer 1

In a deflection bridge circuit, the value of the unknown resistance Rx can be calculated using the balanced state equation R1/R2 = R3/Rx. With the given resistance values, the unknown resistance Rx is 192 Ω.

Step-by-step explanation:

In a deflection bridge circuit, the resistors R1 and R2 are known, while the resistor R3 is variable. To achieve balance in the circuit, the variable resistor R3 is adjusted until the galvanometer reads zero. This means that the potential difference between points b and d is zero, indicating that b and d are at the same potential. With no current running through the galvanometer, it has no effect on the rest of the circuit. Therefore, the branches abc and adc are in parallel, and each branch has the full voltage of the source. Since b and d are at the same potential, the IR drop along ad must equal the IR drop along ab. Thus, R1/R2 = R3/Rx.

Given that R1 = 33 Ω, R2 = 48 Ω, R4 = 192 Ω, and R3 = 132 Ω, we can solve for Rx using the formula R1/R2 = R3/Rx. Rearranging the equation, Rx = (R2 x R3)/R1 = (48 Ω x 132 Ω)/33 Ω = 192 Ω.

So the unknown resistance Rx in the circuit is 192 Ω.