Question

A RLC series circuit has a resistance of 104 ohms, inductance 0.7 H,and Capacitance 6.0 µF. If the amplitude of the voltage supplied by the ac source is 170 V, and the frequency is 60 Hertz, calculate the rms current.

Answer 1

It is a L-C-R circuit  

RMS value is defined as the value of alternating current ( AC) over a complete cycle which would generate same amount of heat in a given resistors that is generated by steady current in the same resistor and in the same time during a complete cycle .

Irms = I_o / ( 2 )^{1/2 - equation 1}

Where I_o is the maximum current in the circuit.

Amplitude of voltage supplied is given

V = V_o sinwt

Where t is time and w is angular frequency.

V_o is maximum voltage in the circuit and it is given = 170 V

Z = V_o / I_{o - equation = 2}

Z is Impedence , it is the total resistance of a circuit applied in the path of a alternating current.

Z = [ R² + ( X_L   - X_C  ) ²  ]^{1/2 - equation 3}

where R is the resistance it is given, R = 104 ohms

X_L is Inductive Reactance and Xc is Capacitive Reactance. Both have same S. I unit as resistance ohm.

X_L = w.L

Where L is inductance and it is given L = 0.7 H

w is angular frequency ,

w = 2.π.f = 2*π*60 =120π , where f is frequency ( Hz)

X_L = 120π x 0.7 = 84 π

Xc = 1/ w. C

Where C is capacitance and it is given = 6uf

Or 6 x 10^-6 f and w is angular frequency

Xc = 1/ (120π) *( 6 x 10^-6 )

Xc = 442.10 ohm

Now put all the values in equation 3

Z = 206.34 ohm

Now use equation 2

Z = Vo/Io

Io = 170 / 206.34

Io = 0.82 A

Use equation 1

Irms = 0.58 A.