Question

An alternating current E(t)=120sin(12t) has been running through a simple circuit for a long time. The circuit has an inductance of L=0.45 henrys, a resistor of R=3ohms and a capacitor of capcitance C=0.036 farads. What is the amplitude of the current I?

Answer 1

To calculate the amplitude of the current in an RLC circuit with given values of inductance, resistance, capacitance, and alternating current, one needs to find the impedance of the circuit first and then apply Ohm's Law to the peak voltage.

Step-by-step explanation:

To find the amplitude of the current I in an RLC circuit with alternating current E(t) = 120sin(12t), we need to calculate the impedance Z of the circuit and apply Ohm's Law to the peak voltage.

First, we find each component's reactance:

Capacitive reactance, XC= 1 / (2πfC)

Inductive reactance, XL = 2πfL

Then, compute the total impedance Z:

Z = √(R2 + (XL - XC)2)

After finding Z, we can determine the amplitude of the current:

I = V0 / Z

Where V0 is the maximum voltage of the source, which is 120 V in this problem.

By plugging in the known values and calculating, we'll get the amplitude of the current I in the circuit.