Two resistors 4 Ω and 6 Ω are in parallel across a 12 V source. What is the total current, and the current through each resistor?

Two resistors 4 Ω and 6 Ω are in parallel across a 12 V source. What is the total current, and the current through each resistor?

• A. I_total = 5 A; I4Ω = 3 A; I6Ω = 2 A
• B. I_total = 4 A; I4 = 2 A; I6 = 2 A
• C. I_total = 6 A; I4 = 4 A; I6 = 2 A
• D. I_total = 5 A; I4 = 2 A; I6 = 3 A

Answer: (A)

In a parallel circuit, the voltage across each resistor is the same as the source, and the currents through the resistors add to give the total current. With a 12 V source, the current through the 4 Ω resistor is 12/4 = 3 A, and through the 6 Ω resistor is 12/6 = 2 A. The total current drawn from the source is 3 + 2 = 5 A. This also checks via the equivalent resistance: 1/R_eq = 1/4 + 1/6 = 5/12, so R_eq = 2.4 Ω, and I_total = 12/2.4 = 5 A. So, total current is 5 A, with 3 A through the 4 Ω resistor and 2 A through the 6 Ω resistor.

In a parallel circuit, the voltage across each resistor is the same as the source, and the currents through the resistors add to give the total current. With a 12 V source, the current through the 4 Ω resistor is 12/4 = 3 A, and through the 6 Ω resistor is 12/6 = 2 A. The total current drawn from the source is 3 + 2 = 5 A. This also checks via the equivalent resistance: 1/R_eq = 1/4 + 1/6 = 5/12, so R_eq = 2.4 Ω, and I_total = 12/2.4 = 5 A. So, total current is 5 A, with 3 A through the 4 Ω resistor and 2 A through the 6 Ω resistor.