A 24-volt source is required to furnish 48 watts to a parallel circuit consisting of four resistors of equal value. What is the voltage drop across each resistor?

Question

A 24-volt source is required to furnish 48 watts to a parallel circuit consisting of four resistors of equal value.  What is the voltage drop across each resistor?

BlackTom AI · Accepted Answer

In a parallel circuit the voltage across each branch equals the source voltage, so each resistor sees the full supply voltage. Key concepts: (1) In parallel circuits, branch voltages are equal to the source voltage. (2) Total power P = V × I_total. (3) For identical parallel resistors, the total current splits equally among branches.

Step-by-step reasoning and calculations:
1. Use total power and source voltage to find total current:
   - P_total = 48 W, V_source = 24 V
   - I_total = P_total / V_source = 48 W / 24 V = 2 A
2. Four equal resistors in parallel share the total current equally:
   - I_per_resistor = I_total / 4 = 2 A / 4 = 0.5 A
3. Determine each resistor’s value (optional check):
   - R_per = V / I_per = 24 V / 0.5 A = 48 Ω
4. Check power per resistor:
   - P_per = V^2 / R = 24^2 / 48 = 576 / 48 = 12 W
   - Total power = 4 × 12 W = 48 W (matches given)

Why the correct answer is correct:
- By the fundamental property of parallel circuits, the voltage across each resistor equals the source voltage, which here is 24 V. The numerical checks above (currents, resistor values, and per-branch power) consistently confirm that each resistor has a 24-volt drop.

Why the other choices are incorrect:
- 12 volts: If each resistor had only 12 V across it while the source is 24 V, that would contradict the parallel-voltage rule. Also, with 12 V per branch the computed power and currents would not match the given total of 48 W.
- 3 volts: Far too small and inconsistent with P = V × I (it would require unrealistically large currents or different circuit topology).

Final confirmation: The voltage drop across each resistor is 24 volts, matching the provided answer.

A 24-volt source is required to furnish 48 watts to a parallel circuit consisting of four resistors of equal value. What is the voltage drop across each resistor?单项选择题

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