In a series LCR circuit connected to an AC source, the rms voltage drops across the resistor, inductor, and capacitor are 40 V , 100 V , and 70 V respectively. If the resistance of the circuit is 20 , what is the rms current in the circuit and the phase angle between the source voltage and the current? (Take 37^ = 3 4 )

Step-by-step solution

The rms current I_ rms is the same through all components in a series circuit. We can find it directly using the voltage drop across the resistor and Ohm's law: I_ rms = V_R R = 40 20 = 2 A The phase angle between the source voltage and the current can be found using the voltage phasor diagram: = V_L - V_C V_R Substitute the given rms voltage drops: = 100 - 70 40 = 30 40 = 3 4 Since 37^ = 3 4 , the phase angle is = 37^ . Answer: 2 A and 37^