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Four identical resistors connected in series with a battery together dissipate 20 W of power. What will be the power dissipated if the same resistors are connected in parallel across the same battery?

Asked in GUJCET 2013 · Heating and power in resistors

• (1) 320 W
• (2) 5 W
• (3) 100 W
• (4) 80 W

Step-by-step solution

Why the other options are wrong

• (2) Divides by 4, as if the parallel connection shared the same power among the resistors: (20)/4 = 5 W. With the same battery P = (V²)/(R_eq), and R_eq falls by a factor of 16, so the power rises.
• (3) No single slip produces 100 W. Sanity check: R_eq changes from 4R to R/4, a factor of 16, so the power becomes 16×20 = 320 W.
• (4) This is the power of just one resistor in the parallel arrangement. In series each resistor dissipated 5 W; in parallel each gets the full battery voltage, four times its old share, so it dissipates 16×5 = 80 W. The four together dissipate 320 W.

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