Question

A torch bulb rated as 4.5 W, 1.5 V is connected in the circuit as shown in the figure. If the bulb glows with maximum intensity, then the emf (E) is nearly

• A. 4.5 V
• B. 1.5 V
• C. 2.67 V
• D. 13.5 V

Hint:

To find the emf, use the relation between power, resistance, and current in circuits with bulbs or resistors.

Answer 1

The Correct Option is C

The power dissipated by the bulb is given by: \[ P = I^2 R \] where \( P = 4.5 \, \text{W} \) and \( V = 1.5 \, \text{V} \). The resistance \( R \) of the bulb can be found using Ohm's law: \[ R = \frac{V^2}{P} = \frac{(1.5)^2}{4.5} = 0.5 \, \Omega \] Now, the total resistance in the circuit is \( R + 1 \, \Omega = 1.5 \, \Omega \). Using the formula for the emf: \[ E = I (R + 1) \] Substituting the values, we find that the emf is 2.67 V.