A series circuit of a 45 Ω resistor, a 2.5 H inductor, and a 36 µF capacitor is connected to source that the emf is given by e = 340 cos(628t-50).

A.Find the sinusoidal expression of the total current.

B.The r.m.s values of the source voltage and the total current

C. The power dissipated in the circuit and the power factor of the circuit.

Question

A series circuit of a 45 Ω resistor, a 2.5 H inductor, and a 36 µF capacitor is connected to source that the emf is given by e = 340 cos(628t-50).

A.Find the sinusoidal expression of the total current.

B.The r.m.s values of the source voltage and the total current

C. The power dissipated in the circuit and the power factor of the circuit.

prathamesh_m · Answer

in such questions u should always start off by finding the inductance:
$$Z=\sqrt{R ^{2}+(X _{L}-X _{C})^{2}}$$

radar · Answer

No need to find the inductance......as it is given

radar · Answer

The 340 is the Peak value of the voltage.  The RMS value is equal to the Peak value divided by sq rt of 2.

Calculate the frequency, I believe that can be obtained from the 628t value provided.

radar · Answer

Convert it to Rad/sec and divide by 2 pi, looks like frequency would be 100 Hz.

Now calculate the reactance offered by the inductor and capacitor and use the Z formula provided by Prathamesh_M to obtain the impedance of the circuit offered to the EMF source.