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Chapter 32: Q. 44 (page 925)

Show that Equation32.27for the phase angleϕof a seriesRLC circuit gives the correct result for a capacitor-only circuit.

Short Answer

Expert verified

The expression ϕ=tan-1XL-XCRfor phase angle of series RLCcircuit gives correct result for capacitor only circuit.

Step by step solution

01

Given Information

We are given that the Equation 32.27which is ϕ=tan-1XL-XCR.

We need to prove that this equation for phase angle of series RLCcircuit gives correct result for capacitor only circuit.

02

Explanation 

We know equation,

tanϕ=VL-VCVR⇒XL-XCRI

Here gets canceled so equation can be rewritten as :

ϕ=tan-1XL-XCR

We are also given that , XL=XC=0

From here phase angle becomesϕ=tan-10=0rad.

Similarly for ACInductor circuit conditions are

localid="1649931138237" R=XC=0ϕ=tan-1∞=π/2rad

Hence proved that it gives correct result for capacitor only circuit.

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Most popular questions from this chapter

An inductor is connected to a 15KHzoscillator. The peak current is 65mAwhen the rms voltage is width="36">6.0V. What is the value of the inductance L?

A series RLC circuit consists of a 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a 2.1mH inductor, and a 550nF capacitor. It is connected to a 50V rms oscillating voltage source with an adjustable frequency. An oscillating magnetic field is observed at a point 2.5mm from the center of one of the circuit wires, which is long and straight. What is the maximum magnetic field amplitude that can be generated?

For what absolute value of the phase angle does a source deliver 75%of the maximum possible power to an RLC circuit?

The peak current through an inductor is 10mA. What is the peak current if

a. The emf frequency is doubled?

b. The emf peak voltage is doubled (at the original frequency)

The resonance frequency of a series RLC circuit is less than the EMF frequency. Does the current lead or lag the EMF? Explain.
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