Question

The equivalent resistance of the circuit is 4 Ω. Calculate the resistance of x.

Answer 1

Equivalent resistance of the circuit R = 4 Ω

Equivalent resistance of 2 Ω and x in series

$$R_1 = 2\Omega + x \quad ...(a)$$

Equivalent resistance of 7 Ω and 5 Ω in series

$$R_2 = 7 + 5 = 12 \Omega$$

As \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2}\) are in parallel

$$\therefore \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$$

$$\frac{1}{4} = \frac{1}{R_1} + \frac{1}{12}$$

$$\frac{1}{R_1} = \frac{1}{4} - \frac{1}{12}$$

$$\frac{1}{R_1} = \frac{2}{12}$$

$$\frac{1}{R_1} = \frac{1}{6}$$

$$\therefore \mathrm{R}_{1} = 6 \Omega$$

Putting the value of \(\mathrm{R}_{1}\) in (a)

$$6 = 2 + x$$

$$\therefore x = 6 - 2 = 4\Omega$$