Chapter 32: 32 - Exercises and Problems (page 925)

For the circuit of FIGURE EX32.32
a. What is the resonance frequency, in both rad/s and Hz?
b. Find $V_{R}$ and $V_{L}$ at resonance.
c. How can $V_{L}$ be larger than $E_{0}$ ? Explain.

Short Answer

Expert verified

a. Resonance frequency in rad/s $= 3125 r a d / s$

Resonance frequency in $H z = 500 H z$

b. $V_{R} = 10 V$ ; $V_{L} = 31.25 V$

c. $V_{c}$ and $V_{L}$ have opposite phases

Step by step solution

Part a) step 1 : Given information

We have to find the resonance frequency

Detailed solution

In a series LCR Circuit, the resonance frequency $f_{R}$ (in Hz) is given by

$f_{R} = \frac{1}{2 π \sqrt{L C}}$

It is given that $L = 10 m H, C = 10 μ F$

Thus,

$f_{R} = \frac{1}{2 π \sqrt{(10 \times 10^{- 3} H) (10 \times 10^{- 6}} F)} = \frac{1}{2 π \sqrt{10^{- 7}}} = \frac{10^{3}}{2 π \times 0.32} \Rightarrow f_{R} = 500 H z$

Now,

$\Rightarrow$ $ω_{r} (r a d / s) = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{10 \times 10^{- 3} \times 10 \times 10^{- 6}}} = \frac{1}{\sqrt{10^{- 7}}} ω_{r} = 3125 r a d / s$

part b) step 1 : Given Information

We have to find $V_{R}$ and $V_{L}$ at resonance.

part b) Step 2 : Detailed solution

As we know , Current = Voltage / Impedence

$I = \frac{V}{\sqrt{R^{2} + (ω L - \frac{1}{ω C}})^{2}} = \frac{10}{\sqrt{10^{2} + {(3125 \times 10 \times 10^{- 3} - \frac{1}{3125 \times 10 \times 10^{- 6}})}^{2}}} ≅ 0.998 A = 1 A$

Now on putting values in respective formulae;

$V_{L} = I X_{L} = I L ω = 1 \times 10^{- 3} \times 3125 = 3125 \times 10^{- 2} = 31.25 V V_{R} = I R = 1 \times 10 = 10 V$

Part c)

The voltage drop across the inductor can be greater than the applied voltage of the a.c because $V_{C}$ and $V_{L}$ have opposite Phases . Thus, $V_{C}$ or $V_{L}$ may be greater than V or $E_{0}$ .

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For the circuit of FIGURE EX32.32
a. What is the resonance frequency, in both rad/s and Hz?
b. Find $V_{R}$ and $V_{L}$ at resonance.
c. How can $V_{L}$ be larger than $E_{0}$ ? Explain.

Short Answer

Step by step solution

Part a) step 1 : Given information

Detailed solution

part b) step 1 : Given Information

part b) Step 2 : Detailed solution

Part c)

One App. One Place for Learning.

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For the circuit of FIGURE EX32.32a. What is the resonance frequency, in both rad/s and Hz?b. Find VRand VL at resonance.c. How can VL be larger than E0? Explain.

Short Answer

Step by step solution

Part a) step 1 : Given information

Detailed solution

part b) step 1 : Given Information

part b) Step 2 : Detailed solution

Part c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Waves Physics

Magnetism

Thermodynamics

Physical Quantities And Units

Engineering Physics

Study anywhere. Anytime. Across all devices.

For the circuit of FIGURE EX32.32
a. What is the resonance frequency, in both rad/s and Hz?
b. Find $V_{R}$ and $V_{L}$ at resonance.
c. How can $V_{L}$ be larger than $E_{0}$ ? Explain.