Bulbs in a Mixed Circuit
Three identical incandescent bulbs, each with resistance 12 Ω when lit, are connected to an ideal 9.0 V battery. Bulb A is in series with a parallel combination of bulbs B and C. An ammeter reads the total current from the battery as 0.50 A. A student notices the ammeter reading is lower than the 0.75 A predicted by treating every bulb as exactly 12 Ω and wonders whether the battery is faulty. The student also claims that because B and C are in parallel they carry the same current as A. The bulbs' resistance depends on filament temperature, which depends on power dissipated.
1. Using the stated 12 Ω per bulb, compute the expected total current and equivalent resistance, then reconcile the measured 0.50 A with the 'faulty battery' claim.
Read the worked answer
B ∥ C: R_BC = 12/2 = 6 Ω. Total R = R_A + R_BC = 12 + 6 = 18 Ω. Expected I = 9.0/18 = 0.50 A - not 0.75 A. The student's 0.75 A likely came from mistakenly adding all three in parallel (12/3 = 4 Ω → 2.25 A) or some other slip; in any case the correct prediction matches the ammeter. The battery is not faulty. This is a judgment about trusting the circuit model over an arithmetic hunch: recompute the equivalent resistance carefully before blaming hardware.
2. Evaluate the claim that B and C carry the same current as A. Then compute the actual currents and the power in each bulb.
Read the worked answer
False. A carries the total current 0.50 A. That current splits equally between identical B and C: 0.25 A each. So I_A = 0.50 A, I_B = I_C = 0.25 A. Power: P_A = I²R = (0.50)²(12) = 3.0 W; P_B = P_C = (0.25)²(12) = 0.75 W. A glows brightest. The parallel branches share the same voltage (V_BC = I_A × R_BC = 0.50 × 6 = 3.0 V), and A drops the remaining 6.0 V - check: 6.0 + 3.0 = 9.0 V.
3. In reality the bulbs' resistances are not equal because they dissipate different powers. Predict qualitatively how the true currents compare to the 12 Ω calculation, and explain the direction of the discrepancy.
Read the worked answer
A dissipates 3.0 W while B and C dissipate 0.75 W, so A's filament is much hotter and its resistance is higher than B's and C's (tungsten resistance rises with temperature). If R_A > 12 Ω and R_B = R_C < 12 Ω, then the series resistance rises and the parallel resistance falls; the total R = R_A + R_BC changes in a way that generally lowers total current below 0.50 A and makes the voltage division shift more toward A. The judgment: the 'identical bulbs' assumption is only a first approximation; real behavior requires recognizing temperature-dependent resistance, and the direction of error follows from which bulb runs hottest.