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

Foundation

Physics Foundation

Ohms Law and Resistance

Heating effect of current electric energy and electric power

Question

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

0.5

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Let mere,

R₁ = 3 + 1 = 4Ω

R₂ = 8Ω

Also, i be the total current in the circuit,
∴ Let i, be current through R₁ and i₂ be current through R₂
∴ current through R₁ is $i_{1} = \frac{i \times R_{2}}{R_{1} + R_{2}} = \frac{i \times 8}{12} = \frac{2 i}{3}$
current through R₂ is $i_{2} = \frac{i \times R_{1}}{R_{1} + R_{2}} = \frac{i \times 4}{12} = \frac{i}{3}$
Let P₁, P₂ be power dissipated in 3Ω and & 8Ω Resistor

∴ $P_{1} = i_{1}^{2} \times 3 P_{2} = i_{2}^{2} \times 8$

∴ $\frac{P_{1}}{P_{2}} = \frac{i_{1}^{2} \times 3}{i_{2}^{2} \times 8} = \frac{(2 i / 3)^{2} \times 3}{(i / 3)^{2} \times 8}$

$\frac{P_{1}}{P_{2}} = \frac{12}{8}$

∴ $\frac{P_{1}}{P_{2}} = \frac{3}{2}$

∴ $P_{1} = \frac{3}{2} \times P_{2}$

∴ $P_{1} = \frac{3}{2} \times 2$ $[\begin{matrix} riven Power dissipated \\ P_{2} = 2 W . for 8 Ω \end{matrix}]$

∴ P₁ = 3 watt