Across the 220 V source of internal resistance 20 , how many lamps of 40 ~W , 100 ~V can be connected in parallel so that all the lamps may glow with full brightness.

Step-by-step solution

Each lamp is rated 40 W at 100 V . The resistance of each lamp is R_L = V^2 P = 100^2 40 = 10000 40 = 250 . Let n be the number of lamps connected in parallel. The equivalent resistance of n lamps is R_p = R_L n = 250 n . The circuit consists of the source voltage V_s = 220 V with internal resistance r = 20 in series with the parallel combination of lamps. For the lamps to glow with full brightness, the voltage across the parallel combination must be 100 V . The current flowing through the circuit is I = V_s - V_L