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# RLC Series Circuit Problems with Solutions

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These questions are related to RL Series Circuit, RC Series Circuit, and RLC Series Circuit. These topics are covered in detail here:

1. Define a series RL circuit:
The combination of a resistor and inductor connected in series to an AC source.
2. Define impedance:
The total opposition to current flow in an AC circuit. Mathematically, it is represented as:

$Z=R+jX$

Where R is a resistance and X represents Reactance.
3. What is the unit of measurement for impedance?
Impedance is measured in Ohms.
4. What is the formula for impedance in an RL Series circuit?
Since, current remains the same through each component in a RC Series circuit, so total impedance can be find by using:

$Z=\frac{{{V}_{s}}}{I}$

Where Vs represents source voltage and I is the total circuit current.
5. With a 5 ohm resistor and a 10 ohm inductive reactance, what is the total impedance?

$Z=\sqrt{{{R}^{2}}+X_{L}^{2}}=\sqrt{{{5}^{2}}+{{10}^{2}}}=11.18\Omega$

6. Define True Power.
True power is measured in watts (W) and is the power drawn by the resistive component of the circuit.
7. What is reactive power?
Reactive power is measured in volt-amperes reactive (VARs) and is defined as the power continually stored and discharged by the magnetic field of the inductive load.
8. What is apparent power?
Apparent power is measured in volt-amperes (VA) and is the combination of the reactive power and true power.

$S=P+jQ$

9. What are the formulas for Power Factor (PF)?

$\text{PF=}\frac{\text{Watts(W)}}{\text{Volt-Ampere(VA)}}\text{=}\frac{\text{True Power}}{\text{Apparent Power}}\text{=}\frac{\text{Resistnce(R)}}{\text{Impedance(Z)}}$

10. Define a series RC circuit.
The total opposition or impedance is due to a combination of both resistance and capacitance reactance.
11. With a 7 ohm resistor and a 10 ohm capacitance reactance, what is the total impedance?

$Z=\sqrt{{{R}^{2}}+X_{C}^{2}}=\sqrt{{{7}^{2}}+{{10}^{2}}}=12.21\Omega$

12. What is the formula for total impedance in a RLC circuit?

${{Z}_{T}}=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}$

13. What is a resonant circuit?
It is a circuit with inductive reactance equal to capacitance reactance and can be series or parallel.

${{X}_{L}}={{X}_{C}}$

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