The ac generator in a series RCL circuit has an rms voltage of 70.9 V. The values of the resistance, capacitive reactance, and inductive reactance are, respectively, R = 30.0 Ω, XC = 50.0 Ω, and XL = 90.0 Ω. What is the rms current in the circuit?

The RMS current in the circuit is 1.418 A

Explanation:

The equation of the impedance of an RCL circuit is equal to:

Z = (R^2 + (XL - XC)^2)^1/2

Z = (30^2 + (50-90)^2)^1/2 = 50 ohms

To calculate the RMS current we must use Ohms' law, therefore:

I = V/Z = 70.9/50 = 1.418 A

1.418 A

Explanation:

From Alternating current,

V = IZ Equation 1

Where V = rms Voltage, I = rms current, Z = Impedance of the RLC circuit.

make I the subject of the equation

I = V/Z Equation 2

But,

Z = √[(XL-Xc)²+R²] Equation 3

Where XL = inductive reactance, Xc = capacitive reactance,  R = resistance

Substitute equation 3 into equation 2

I = V/√[(XL-Xc)²+R²] Equation 4

Given: V = 70.9 V, XL = 90 Ω, Xc = 50 Ω, R = 30 Ω

I = 70.9/√[(90-50)²+30²]

I = 70.9/√(40²+30²)

I = 70.9/√(1600+900)

I = 70.9/√2500

I = 70.9/50

I = 1.418 A