Question

The minimum number of identical bulbs of rating 4V, 6W, that can work safely with desired brightness, when connected in series with a 240V mains supply is:

• A. 20
• B. 40
• C. 60
• D. 80

Hint:

To calculate the total number of bulbs in series for a given voltage, you need to first find the resistance of each bulb and then use the total voltage.

Answer 1

The Correct Option is B

For a bulb of rating 4V, 6W, we can calculate the resistance using the formula: \[ P = \frac{V^2}{R} \] Thus, \( R = \frac{V^2}{P} = \frac{4^2}{6} = \frac{16}{6} \approx 2.67 \, \Omega \). Now, to operate safely with a 240V mains supply, the total resistance in the series connection must be: \[ R_{{total}} = \frac{V_{{total}}^2}{P_{{total}}} \] For total power 6W per bulb, and for the total power at 240V, the number of bulbs required can be calculated to be 40. 
Thus, the correct answer is option (b).