A 100Ω resistor and a 200Ω resistor are connected in parallel to the same 12V battery. Which resistor dissipates more power?
AThe 200Ω resistor — more resistance means more power dissipated
BThe 100Ω resistor — in a parallel circuit with fixed voltage, lower resistance draws more current and dissipates more power
CBoth dissipate equal power — they are connected to the same voltage source
DThe 200Ω resistor — it allows less current to flow, which concentrates the energy
In a parallel circuit, all branches share the same voltage (12V here). The appropriate power formula is P = V²/R: with fixed V, power decreases as resistance increases. P₁₀₀ = 144/100 = 1.44W; P₂₀₀ = 144/200 = 0.72W. The 100Ω resistor dissipates twice as much power. The critical misconception (option A) is that 'more resistance = more power' — this is true in a series circuit where current is fixed (P = I²R), but exactly backwards in a parallel circuit where voltage is fixed. Choosing the wrong formula because you forgot which quantity is held constant is the most common error in power calculations.
Question 2 Multiple Choice
A high-voltage power transmission line carries 1000 MW of power at 500,000 V. If the transmission voltage were cut to 50,000 V (one-tenth as high) while delivering the same power, what would happen to resistive losses in the transmission lines?
ALosses would decrease by a factor of 10 — lower voltage means less electrical stress on the insulation
BLosses would stay the same — the same amount of power is being delivered regardless of voltage
CLosses would increase by a factor of 100 — the required current increases tenfold, and losses scale as I²
DLosses would double — current doubles when voltage halves
Power = IV, so delivering the same power at one-tenth the voltage requires ten times the current (I = P/V). Resistive losses in the transmission lines scale as I²R. If I increases by 10×, then I² increases by 100×, so losses increase by a factor of 100. This is precisely why power is transmitted at very high voltages — the I²R relationship means small reductions in current produce large reductions in transmission loss. Halving current cuts losses by 75%; the 500kV → 50V comparison here is a 100-fold increase in losses, making lower-voltage long-distance transmission economically and physically impractical.
Question 3 True / False
In Joule heating, reversing the direction of current through a resistor causes the resistor to absorb heat rather than generate it.
TTrue
FFalse
Answer: False
Joule heating always generates heat regardless of current direction, because power dissipated is P = I²R — the current is squared, so it's always positive. Whether current flows left-to-right or right-to-left, the resistor converts electrical energy to heat. This distinguishes Joule heating from energy storage elements: a capacitor stores energy (charge/discharge), and an inductor stores energy (magnetic field build-up/collapse), but a resistor always dissipates — it can never return electrical energy to the circuit. Joule heating is irreversible by nature.
Question 4 True / False
Electric power and electric energy are different quantities: power is the rate at which energy is consumed, while energy is the total amount consumed over time.
TTrue
FFalse
Answer: True
Power (P, measured in watts) and energy (E, measured in joules or kilowatt-hours) are related by E = P × t. A 100W light bulb operating for 10 hours consumes E = 100W × 10h = 1000 Wh = 1 kWh of energy. The distinction matters practically: utility companies bill for energy (kWh), not power (watts). A device with a high wattage rating but short usage time may consume less total energy than a low-wattage device running continuously. Confusing the two leads to errors in circuit analysis — a 60W bulb doesn't 'use' 60 joules; it converts 60 joules per second.
Question 5 Short Answer
Why is the statement 'P = I²R means more resistance always dissipates more power' sometimes correct and sometimes exactly backwards? Explain when each case applies.
Think about your answer, then reveal below.
Model answer: P = I²R applies when current I is fixed — typically in a series circuit, where all elements carry the same current. With fixed I, doubling R doubles power. P = V²/R applies when voltage V is fixed — typically in a parallel circuit, where all elements share the same voltage. With fixed V, doubling R halves power. The direction of the relationship reverses depending on what the circuit holds constant. 'More resistance = more power' is true in series (fixed I), and 'more resistance = less power' is true in parallel (fixed V).
This is the most important nuance in power calculations. Both P = I²R and P = V²/R are always mathematically true for a resistor, but they give different intuitions because they assume different variables are held constant. In a series circuit, current is the same through all elements (Kirchhoff's current law for a single loop), so I²R is the natural formula. In a parallel circuit, voltage is the same across all branches, so V²/R is the natural formula. Using the wrong one doesn't give a math error — it gives a valid calculation for the wrong scenario.