Question

Power dissipated across the 8 ohm resistor in the circuit shown here is 2 watt. The power dissipated in watt units across the 3 ohm resistor is

Answer 1

The power dissipated in watt units across the 3Ω resistor is 3 Watt.

Explanation:

• R1 = 3 + 1 = 4 Ω
• R2 = 8 Ω

Let i b the total current in the circuit.

Current through R1 "i1" = i x R2 / R1 + R2 = i x 8 / 12 = 2i / 3

Current through R2 is i2 =   i x R1 / R1 + R2 = 1 x 4 / 12 = i / 3

Power dissipated in 3 Ω resistor is.

P1 = i1^2 x 3    ---- (1)

Power dissipated in 8 Ω resistor is.

P2 = i2^2 x 8   ----(2)

P1 / P2 =  i1^2 x 3 / i2^2 x 8

P1 / P2 =  (2i / 3)^2 x 3 / (i / 3)^2 x 8 = 12/8 = 3/2

P1 = 3/2 x P2 = 3/2 x  2 = 3 Watt

Hence the power dissipated in watt units across the 3Ω resistor is 3 Watt.

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