Question

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ______ min.

Options

• 15

• 16

• 20

• 10

Answer 1

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be 15 min.

Explanation:

Let there be two coils A and B. Let the potential difference across source be V

Using H = `"V"^2/"R""t"`

For Coil (1) H = `"V"^2/"R"^1xx60`     ...(1)

For Coil (2) H = `"V"^2/"R"^2xx20`     ...(2)

When coils (1) and (2) connected in parallel combination across voltage source.

Total Heat generated = H₁ + H₂

Let the total time be ‘t’ when two coils together in parallel are operated.

As  H_total = H

⇒ H = `"V"^2/"R"_1 "t" + "V"^2/"R"_2"t"` 

H = `"H"/60 "t" + "H"/20"t"`    ...From equation (1) and (2)

1 = `(1/60+1/20)"t"`

⇒ t = `1200/80`

= 15 minutes.