Question

In the bridge circuit shown, the voltmeter \( V \) showed zero when the value of the resistors are: \( R_1 = 100 \, \Omega \), \( R_2 = 110 \, \Omega \), and \( R_3 = 90 \, \Omega \). If \( \frac{R_1}{R_2} = \frac{R_A}{R_B} \), the value of \( R_4 \) in ohm is \(\underline{\hspace{2cm}}\). 

Hint:

In a balanced bridge, use the ratio of resistances to find the unknown resistor value.

Answer 1

Correct Answer: 99

In a balanced bridge circuit, when the voltmeter reads zero, the ratio of resistances is given by: \[ \frac{R_1}{R_2} = \frac{R_A}{R_B}. \] Substituting the given values: \[ \frac{R_1}{R_2} = \frac{100}{110} = \frac{R_A}{R_B}. \] Since \( R_A = 1 \, \Omega \), we get: \[ \frac{100}{110} = \frac{1}{R_B}, R_B = \frac{110}{100} = 1.1 \, \Omega. \] Thus, \( R_4 = 99 \, \Omega \).