Physics – 4.3.2 Series and parallel circuits | e-Consult
4.3.2 Series and parallel circuits (1 questions)
1. Calculate the equivalent resistance of the parallel combination:
1 / Req = 1 / R1 + 1 / R2 + 1 / R3
1 / Req = 1 / 12Ω + 1 / 24Ω + 1 / 48Ω
1 / Req = (4 + 2 + 1) / 48Ω = 7 / 48Ω
Req = 48Ω / 7 ≈ 6.86Ω
2. Calculate the total current using Ohm's Law (I = V / R):
Itotal = V / Req = 12V / 6.86Ω ≈ 1.75A
Explanation: The total current (1.75A) is greater than the current through each resistor (I1 = V/R1 = 12V/12Ω = 1A, I2 = V/R2 = 12V/24Ω = 0.5A, I3 = V/R3 = 12V/48Ω = 0.25A) because the voltage is divided equally across each branch in a parallel circuit. The equivalent resistance of the parallel combination is less than the resistance of any individual resistor. A lower equivalent resistance means a larger total current for a given voltage, as per Ohm's Law (I = V/R). The current in each branch is inversely proportional to its resistance; therefore, branches with lower resistance will carry more current. The total current is the sum of these individual currents, resulting in a larger value than the current in any single branch.