Under which of the following cases, the power dissipated in R₃ in the circuit shown will increase?

Concept:

The power dissipated by the resistor is given by:

P = I²R

I = Current flowing across the resistor

R = Resistance of the resistor

The power dissipated by the resistor is directly proportional to the square of the current, i.e.

P ∝ I²

Analysis:

The net current flowing across the circuit is given by:

\(I=\frac{E}{R_{eq}}\)

R_eq = R₁ + R₂ + R₃ + R₄

\(I=\frac{E}{R_1+R_2+R_3+R_4}\)

The power dissipated in R₃ is:

P_R3 = I² × R₃

\(P_{R3}=(\frac{E}{R_1+R_2+R_3+R_4})^2 \times R_3\)

Observation:

• We observe that the power will decrease with an increase in R₁ or R₂ or R₄.
• With a decrease in E, the power dissipated will decrease.
• It is only when R₄ is short-circuited, i.e. when R₄ = 0, the power dissipated will increase.