Several lamps of 50 ~W and 100 ~V rating are available. How many of them can be connected in parallel across a battery of a 120 ~V of internal resistance 10 , so that all bulbs glow in full power?

Step-by-step solution

According to given condition, let n number of bulbs are connected in parallel as shown below aligned Resistance of each bulb, R &= V² P [ P= V² R ] &= 100² 50 =200 aligned Using KVL in the lowest loop, array ll & 120-10 I- I n 200=0 & 12-I= 20 I n ...(i) array Power delivered by battery = Sum of power used in bulbs (120-10 I) I=50 n array rlr & (12-I) I=5 n & & 20 I n I =5 n array [from Eq. (i)] 4 I²=n² I= n 2 ...(ii) From Eqs. (i) and (ii), we get 12- n 2 = 20 n n 2 n=4