Chapter 32: Q. 20 (page 924)

A high-pass filter consists of a $1.59 m F$ capacitor in series with a $100 Ω$ resistor. The circuit is driven by an $A C$ source with a peak voltage of $5.00 V$ .
a. What is the crossover frequency $f_{c}$ ?
b. What is $V_{R}$ when $f = \frac{1}{2} f_{c}, f_{c}$ , and $2 f_{c}$ ?

Short Answer

Expert verified

(a) Crossover frequency , $f_{c} = 1000 Hz$

(b) Value of $V_{R} = 3.54 V$

Step by step solution

AC Source

The flow of electrical charge that occasionally reverses direction is understood as electricity (ac).

As mentioned in Induced Electric Fields, an alternating emf generated in an exceedingly very station produces an ac.

An ac circuit is one during which the ac source varies frequently, often sinusoidally.

Find Crossover frequency

Given values

$C = 1.59 \times 10^{- 6} F$ (farad)

$R = 100 Ω$ (ohm)

$ε_{o} = 5.00 V$ (voltage)

we use formula

$w = \frac{1}{R C}$

Derive from the formula,

$w = \frac{1}{R C}$

$2 π f_{c} = \frac{1}{R C}$

$f_{c} = \frac{1}{2 π R C}$

localid="1650213173701" $f_{c} = \frac{1}{2 π \times (100) Ω \times (1.59 \times 10^{- 6}) F}$

$f_{c} = 1000 Hz$

Find value of voltage

$V_{R} = \frac{ε_{o} R}{\sqrt{R^{2} + \frac{1}{w^{2} C^{2}}}}$

$V_{R} = \frac{ε_{o} R}{R^{2} + \frac{R^{2} C^{2}}{C^{2}}}$

Substitute the values,

$V_{R} = \frac{5.00 V}{1.41}$

$V_{R} = 3.54 V$

$f = f_{c} \Rightarrow V_{R}^{'} = \frac{ε_{o}}{\sqrt{2}}$

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A high-pass filter consists of a $1.59 m F$ capacitor in series with a $100 Ω$ resistor. The circuit is driven by an $A C$ source with a peak voltage of $5.00 V$ .
a. What is the crossover frequency $f_{c}$ ?
b. What is $V_{R}$ when $f = \frac{1}{2} f_{c}, f_{c}$ , and $2 f_{c}$ ?

Short Answer

Step by step solution

AC Source

Find Crossover frequency

Find value of voltage

One App. One Place for Learning.

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A high-pass filter consists of a 1.59mFcapacitor in series with a 100Ωresistor. The circuit is driven by an ACsource with a peak voltage of 5.00V. a. What is the crossover frequency fc? b. What is VRwhen f=12fc,fc, and 2fc?

Short Answer

Step by step solution

AC Source

Find Crossover frequency

Find value of voltage

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Turning Points in Physics

Fluids

Thermodynamics

Particle Model of Matter

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.

A high-pass filter consists of a $1.59 m F$ capacitor in series with a $100 Ω$ resistor. The circuit is driven by an $A C$ source with a peak voltage of $5.00 V$ .
a. What is the crossover frequency $f_{c}$ ?
b. What is $V_{R}$ when $f = \frac{1}{2} f_{c}, f_{c}$ , and $2 f_{c}$ ?