Physics Current Electricity UHS 2022
PMDC Verified Question 56 of 112
A low voltage supply with an e.m.f of 20 V and an internal resistance of 1.5 ohms is used to supply power to a heater of resistance 6.5 ohms in a fish tank. What is the power supplied to the water in the fish tank?
A
41 W
B
50 W
C
53 W
D
62 W
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: 41 W
Concept:

Power supplied to the water is the power dissipated specifically by the external heater.

Formula:

$$ I = \frac{E}{R + r} \quad \text{and} \quad P = I^2 R $$

Solution:

  • Calculate total current: \( I = \frac{20 \text{ V}}{6.5 \, \Omega + 1.5 \, \Omega} = \frac{20}{8} = 2.5 \text{ A} \).


  • Calculate power dissipated by the heater (external resistance \( R = 6.5 \, \Omega \)):


  • \( P = (2.5)^2 \times 6.5 = 6.25 \times 6.5 = 40.625 \text{ W} \).


  • Rounding to the nearest whole number gives approx 41 W.


Why other options are incorrect:

  • Opt B: 50W is the total power generated by the source (\( P = E \times I = 20 \times 2.5 = 50\text{W} \)), but this includes heat lost inside the battery.

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