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# Calculating Equivalent Resistance in a Parallel Circuit: Resistor R_eq

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Question: An 18.0 Ω, 14.0 Ω, and 7.00 Ω resistor are connected in parallel to an emf source. A current of 5.00 A is in the 14.0 Ω resistor. Calculate the equivalent resistance of the circuit.

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When resistors are connected in parallel, they share the same potential difference (voltage). The total current flowing into the junction, or from the battery, is the sum of the current flowing through each parallel branch. Given: - Current across 14 Ohm resistor, I14 = 5A - Voltage across 14 Ohm resistor, V14 = I14 * R14 = 5A * 14Ω = 70V This same voltage will appear across the other two resistors (18Ω and 7Ω) as they are in parallel. Therefore, the currents through the individual resistors, I18 and I7, can be calculated using Ohm's law (V = IR): - Current across 18 Ohm resistor, I18 = V14 / R18 = 70V / 18Ω ≈ 3.89A - Current across 7 Ohm resistor, I7 = V14 / R7 = 70V / 7Ω ≈ 10A The total current, I_total, is the sum of the three currents: I_total = I14 + I18 + I7 = 5A + 3.89A + 10A = 18.89A The equivalent resistance of resistors connected in parallel is given by: 1/Requiv = 1/R1 + 1/R2 + 1/R3 So, 1/Requiv = 1/18Ω + 1/14Ω + 1/7Ω = 0.0556 + 0.0714 + 0.1429 = 0.2699 Ω^-1 Now, by taking the reciprocal to get Requiv, you have: Requiv = 1/0.2699 = 3.704 Ohm approximately. So, the equivalent resistance of the circuit should be about 3.70 Ohm.

April 5, 2024, 8:03 a.m.

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