Suppose voltage V is applied across a resistance R. The power dissipated in the resistance is P. Now the same voltage V is applied across a parallel combination of three equal resistors each of resistance R. Then the power dissipated in the second case will be

In the first case, power dissipated by a single resistor R under voltage V is given by the formula P = V²/R [2]. When three equal resistors of resistance R are connected in parallel, the equivalent resistance (Rp) of the combination is calculated using the reciprocal sum rule: 1/Rp = 1/R + 1/R + 1/R, which simplifies to Rp = R/3 [2]. In a parallel circuit, the voltage across each resistor remains the same as the source voltage V [3]. The total power dissipated in the second case is calculated using the same voltage V across the new equivalent resistance: P' = V²/Rp = V²/(R/3) = 3(V²/R). Since P = V²/R, the new power dissipation is 3P [1]. This demonstrates that adding identical resistors in parallel reduces total resistance and increases total power dissipation proportionally [1].

Sources

1. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192
2. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186
3. [3] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 185