Question

A coil in the heater consumes power P on passing current. If it is cut into halves and joined in parallel, it will consume power:

Options

• P

• `"P"/2`

• 2P

• 4P

Answer 1

4P

Explanation:

Original power consumed, P = `"V"^2/"R"`

When used in parallel

`1/"R"_"P" = 1/"R"_1 + 1/"R"_2 = 1/("R"/2) + 1/("R"/2) = 4/"R"`

R_P = `"R"/4`

∴ New power consumed when two halves in parallel

P' = `"V"^2/"R"_"P" = "V"^2/("R"/4) = (4 "V"^2)/"R"` = 4P