Chapter 4: Q21E (page 1045)

(a) Show that for an L-R-C series circuit the power factor is equal to $\frac{R}{Z}$ (b) An L-R-C series circuit has phase angle $- 31.5 °$ . The voltage amplitude of the source is 90.0 V. What is the voltage amplitude across the resistor?

Short Answer

Expert verified

The power factor is equal to $\frac{R}{Z}$ and the voltage amplitude across the resistor is 76.7V.

Step by step solution

Step-1: Power factor definition

The power factor is the cos of the phase angle of the voltage with respect to the current.

Step-2: Calculations for power factor formula

$From figure, cosϕ = \frac{IR}{IZ} = \frac{R}{Z}$

Therefore, the formula for power factor is $\frac{R}{Z}$

Step-3: Calculations for voltage amplitude of the resistor

Since the phase angle given is negative, therefore the phase angle is negative, which means that the voltage lags the current. In part(a),the term IZ represents the voltage amplitude in the circuit and it is given by 90V. So, we can get the voltage amplitude of the resistor $V_{R}$ as next

$V_{R} = I R = \frac{V}{Z} (R) = (V) \frac{R}{Z} = (V) \cos ϕ = (90 V) \cos (- 31.5 °) = 76.7 V$

Hence, the power factor is $\frac{R}{Z}$ and the resistor voltage amplitude is 76.7V.

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(a) Show that for an L-R-C series circuit the power factor is equal to $\frac{R}{Z}$ (b) An L-R-C series circuit has phase angle $- 31.5 °$ . The voltage amplitude of the source is 90.0 V. What is the voltage amplitude across the resistor?

Short Answer

Step by step solution

Step-1: Power factor definition

Step-2: Calculations for power factor formula

Step-3: Calculations for voltage amplitude of the resistor

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(a) Show that for an L-R-C series circuit the power factor is equal toRZ(b) An L-R-C series circuit has phase angle-31.5°. The voltage amplitude of the source is 90.0 V. What is the voltage amplitude across the resistor?

Short Answer

Step by step solution

Step-1: Power factor definition

Step-2: Calculations for power factor formula

Step-3: Calculations for voltage amplitude of the resistor

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

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Study anywhere. Anytime. Across all devices.

(a) Show that for an L-R-C series circuit the power factor is equal to $\frac{R}{Z}$ (b) An L-R-C series circuit has phase angle $- 31.5 °$ . The voltage amplitude of the source is 90.0 V. What is the voltage amplitude across the resistor?