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Question
How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?
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Solution
Suppose n resistors of resistance 176 Ω are connected in parallel.
Therefore, the value of equivalent resistance (Rp) will be:
`1/"R"_"p" = 1/176 + 1/176 + ... + "n"`
`1/"R"_"p" = "n". (1/176)`
Rp = `176/"n"` Ω ......(1)
Given, V = 220 V and I = 5 A
∴ According to Ohm's law: Rp = `"V"/"I"`
= `220/5`
= 44 Ω
By substituting the value of Rp in equation (1), we get:
44 = `176/"n"`
n = `176/44`
n = 4
Hence, the number of resistors (n) is 4.
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