Power dissipated across the `8 Omega` in the circuit shown here is `2 W`. The power dissiated in watt units across the `3 Omega` is

Options

A. 2
B. 1
C. 0.5
D. 3

Answer

D

Explanation

(d) Resistance `1 Omega` and `3 Omega` are connected in series, so effecitve resistance
`R' = 1 + 3 = 4 Omega`
Now, `R'` and `8 Omega` are in parallel. We know that potential difference across resistance in parallel order is the same
Hence, `R' xx i_(1) = 8 i_(2)`
or `4 xx i_(1) = 8 i_(2)` or `i_(1) = (80)/(4) i_(2) = 2 i_(2)`
or `i_(1) = 2 i_(2)`
Power dissipated across `8 Omega` resistance is
`i_(2)^(2) (8)t = 2 W`
or `i_(2)^(2) t = (2)/(8) = 0.25 W`
Power dissipated across `3 Omega` resistance is
`H = i_(1)^(2) (3) t = (2 i_(2))^(2) (3) t = 12 i_(2)^(2) t`
But `i_(2)^(2) t = 0.25 W`
`H = 12 xx 0.25 = 3 W`