# Find power when resistor, capacitor, and inductor are connected in a series

• jamiewilliams
In summary, the average power delivered to a resistor connected to an AC generator is 0.952 W. When a capacitor is added in series, the power decreases to 0.477 W and when an inductor is added, it decreases further to 0.255 W. To determine the power dissipated when both the capacitor and inductor are added, the equations for impedance and power (P(1), P(2), P(3)) must be used to relate R, XC, and XL to the powers P1, P2, and P3. The final answer is 0.666 W.
jamiewilliams

## Homework Statement

When a resistor is connected by itself to an ac generator, the average power delivered to the resistor is 0.952 W. When a capacitor is added in series with the resistor, the power delivered is 0.477 W. When an inductor is added in series with the resistor (without the capacitor), the power delivered is 0.255 W. Determine the power dissipated when both the capacitor and the inductor are added in series with the resistor. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

## Homework Equations

P(1)= (V^2)/(R)
P(2)= (V^2*R)/Z^2)
P(3)= (V^2*R)/(R^2+(X(L)-X(C))

## The Attempt at a Solution

I am having trouble setting up the equation for P(4). I know the answer is .666W but cannot manipulate the equations to get the right answer.

Express the impedances in terms of R, Xc and XL for all cases and use the "relevant equations" to relate R, XC, XL to the powers P1, P2, P3. ehild

## 1. How do I calculate the total impedance in a series circuit with a resistor, capacitor, and inductor?

The total impedance in a series circuit with a resistor, capacitor, and inductor can be calculated using the following formula: Ztotal = √(R² + (Xl - Xc)²). R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance.

## 2. What is the phase relationship between voltage and current in a series circuit with a resistor, capacitor, and inductor?

In a series circuit with a resistor, capacitor, and inductor, the voltage and current have a phase difference of 90 degrees. This means that the voltage and current are out of phase with each other.

## 3. How does the presence of a capacitor and inductor affect the overall power in a series circuit?

The presence of a capacitor and inductor in a series circuit can affect the overall power by causing the circuit to have a reactive power component. This reactive power does not contribute to the actual work done by the circuit, but it does affect the overall power factor.

## 4. Can the total power in a series circuit with a resistor, capacitor, and inductor ever be negative?

No, the total power in a series circuit with a resistor, capacitor, and inductor cannot be negative. Power is always a positive quantity, representing the amount of work done by the circuit.

## 5. How do I calculate the power factor in a series circuit with a resistor, capacitor, and inductor?

The power factor in a series circuit with a resistor, capacitor, and inductor can be calculated using the following formula: PF = cos(θ) = R/Ztotal, where θ is the phase angle between the voltage and current and Ztotal is the total impedance of the circuit.

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