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?

NCERT Question 12 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?
Given
Potential difference = V = 220 V
Power of each bulb = P = 10 W
Current = I = 5 A
Let the number of bulb = n
First we’ll find the resistance of each bulb
We know that
P = V I
P = V × 𝑉/𝑅
P = 𝑉^2/𝑅
R = 𝑉^2/𝑃
R = (220)^2/10
R = 48400/10
R = 4840 Ω
Resistance of 1 bulb = 4840 Ω
V = I R
𝑉/𝑅 = I
For a flow of 5 A current, we need to find the equivalent resistance of the circuit
By Ohm’s law
V = I RE
RE = 𝑉/𝐼
RE = 220/5
RE = 44 Ω
We know that,
In parallel combination,
equivalent resistance is given by
1/𝑅_𝑝 = 1/𝑅_1 + 1/𝑅_2 + 1/𝑅_3 + … …
∴ 1/𝑅_𝐸 = 1/𝑅 + 1/𝑅 + 1/𝑅 + … … (n times)
1/𝑅_𝐸 = n × 1/𝑅
1/44 = n × 1/4840
∴ n = 4840/44
n = 1210/11
n = 110
∴ 110 bulbs have to connected in parallel

CA Maninder Singh is a Chartered Accountant for the past 13 years and a teacher from the past 17 years. He teaches Science, Economics, Accounting and English at Teachoo

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