Question

How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?

Answer 1

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)`

R_p = `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.