[long_answer] Three resistors of 5 Ω, 10 Ω, and 15 Ω are connected in series across a 30 V supply. (a) Calculate the current through the circuit and the potential difference across each resistor. (b) Which resistor dissipates the most power? Justify using an appropriate formula. (c) If the 15 Ω resistor is now removed and the remaining two resistors stay connected in series to the same 30 V supply, how does the power dissipated in the 5 Ω resistor change? Support your answer with calculations.
Generated by claude-sonnet-4-6 · 2026-06-26 01:11 · grounding rag
Model Answer
(a) Current and potential difference:
Total resistance: $R_s = 5 + 10 + 15 = 30\ \Omega$
Current: $I = V/R_s = 30/30 = \mathbf{1\ A}$
Potential difference across each resistor (V = IR):
- $V_1 = 1 \times 5 = \mathbf{5\ V}$
- $V_2 = 1 \times 10 = \mathbf{10\ V}$
- $V_3 = 1 \times 15 = \mathbf{15\ V}$
(b) Resistor dissipating most power:
Using $P = I^2R$ (current is same in series):
- $P_1 = 1^2 \times 5 = 5\ \text{W}$
- $P_2 = 1^2 \times 10 = 10\ \text{W}$
- $P_3 = 1^2 \times 15 = \mathbf{15\ W}$
The 15 Ω resistor dissipates the most power. In a series circuit, since current is constant, $P \propto R$, so the largest resistor dissipates maximum power.
(c) Change in power dissipated in 5 Ω resistor:
New circuit: 5 Ω and 10 Ω in series, V = 30 V
New total resistance: $R_s = 5 + 10 = 15\ \Omega$
New current: $I' = 30/15 = 2\ \text{A}$
New power in 5 Ω: $P' = I'^2 \times 5 = 4 \times 5 = \mathbf{20\ W}$
Previously, $P = 1^2 \times 5 = 5\ \text{W}$. The power dissipated in the 5 Ω resistor increases from 5 W to 20 W (4 times) because removing the 15 Ω resistor reduces total resistance, increasing current.
Source: Chapter 11, Sections 11.6.1 and 11.8
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Explanation
- Examiners award 1 mark each for correct $R_s$ and $I$ in part (a), and 1 mark for all three V values.
- In part (b), you must quote the formula $P = I^2R$ and state why the largest R wins (same I throughout series circuit).
- In part (c), you must recalculate both current and power — just stating "power increases" without numbers earns no marks. Show the before and after comparison explicitly.