A series circuit has R = 8 Ω and X_L = 6 Ω. If the supply is 120 V RMS, what is the current?

A series circuit has R = 8 Ω and X_L = 6 Ω. If the supply is 120 V RMS, what is the current?

• A. 10 A
• B. 12 A
• C. 8 A
• D. 15 A

Answer: (B)

In an AC series circuit, the current is determined by the total impedance, which combines resistance and inductive reactance as Z = sqrt(R^2 + X_L^2). The current magnitude is I = V / Z. Here, Z = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 Ω. With a supply of 120 V RMS, the current is I = 120 / 10 = 12 A. The current lags the voltage by an angle φ where tan φ = X_L / R = 6/8 = 0.75, so φ ≈ 36.9 degrees.

In an AC series circuit, the current is determined by the total impedance, which combines resistance and inductive reactance as Z = sqrt(R^2 + X_L^2). The current magnitude is I = V / Z.

Here, Z = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 Ω. With a supply of 120 V RMS, the current is I = 120 / 10 = 12 A.

The current lags the voltage by an angle φ where tan φ = X_L / R = 6/8 = 0.75, so φ ≈ 36.9 degrees.