Two resistors, 20 $\Omega$ and 30 $\Omega$, are connected in parallel. A third resistor, 24 $\Omega$, is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The current through the 30- $\Omega$ resistor is

Question

Two resistors, 20  $\Omega$ and 30  $\Omega$, are connected in parallel. A third resistor, 24  $\Omega$, is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The current through the 30- $\Omega$ resistor is

Quizplus · Accepted Answer

The total resistance of the parallel combination of the 20-ohm and 30-ohm resistors can be calculated using the formula for parallel resistors: 1/R_total = 1/R1 + 1/R2. This gives a combined resistance of 12 ohms for the parallel part. Adding the 24-ohm resistor in series gives a total circuit resistance of 36 ohms. The total current from the power source is then I = V/R = 36V / 36Ω = 1A. The voltage across the parallel combination is the same as the voltage across the 30-ohm resistor, which is the full battery voltage of 36V (since it's in series with the 24-ohm resistor). The current through the 30-ohm resistor is then I = V/R = 36V / 30Ω = 1.2A, but since the total current in the circuit is 1A and it splits between the two parallel resistors, we need to calculate the current distribution correctly. The error in the explanation here is in the calculation of the current through the 30-ohm resistor given the total current and the parallel combination. Correctly, the current through the 30-ohm resistor is found by using the voltage across it (which is the same as the voltage across the parallel combination) and its resistance. The voltage across the parallel combination is the current through the series resistor (1A) times its resistance (24 ohms), which incorrectly calculates the voltage across the parallel combination. The correct approach is to recognize that the voltage across the parallel combination is part of the total voltage and is determined by the proportion of resistances. The mistake in the explanation involves incorrect voltage calculation across the parallel resistors and misunderstanding the distribution of current. Correctly, the current through the 30-ohm resistor is determined by the total current divided proportionally by the resistance values in the parallel circuit, not by an incorrect application of Ohm's law with a miscalculated voltage. The correct calculation involves understanding that the total current (1A) is divided among the parallel resistors based on their resistances, leading to the correct answer for the current through the 30-ohm resistor.

Two Resistors, 20 Ω\OmegaΩ And 30 Ω\OmegaΩ , Are Connected in Parallel Ω\OmegaΩ

Two Resistors, 20 $\Omega$ And 30 $\Omega$ , Are Connected in Parallel $\Omega$