Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A?
110 lamps can be connected in parallel.
Explanation
This problem involves understanding parallel connections and power-current relationship. Each bulb rated 10 W at 220 V draws a specific current. When connected in parallel, all bulbs get the same voltage (220 V), and the total current is the sum of individual currents. The maximum number of bulbs is determined by dividing the maximum allowable current by the current drawn by one bulb.
Solution Steps
Step 1: Given values - Voltage (V) = 220 V, Power rating of each bulb (P) = 10 W, Maximum allowable current (I_max) = 5 A
Step 2: Calculate current drawn by one bulb using P = VI, which gives I = P/V = 10/220 = 1/22 A
Step 3: When lamps are connected in parallel, each lamp operates at 220 V and draws the same current of 1/22 A
Step 4: If n lamps are connected in parallel, total current drawn = n × (1/22) A
Step 5: For maximum allowable current: n × (1/22) = 5, solving: n = = 110