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Chapter 32: Q. 8 (page 924)

A $0.30 渭 F$ capacitor is connected across an AC generator that produces a peak voltage of $10 V$ . What is the peak current to and from the capacitor if the emf frequency is
(a) $100 H z$ ?
(b) $100 k H z$ ?

Short Answer

Expert verified

$(a) I_{o} = 1.9 脳 10^{- 3} A$

role="math" localid="1649956592903" $(b) 鈥� I_{o} = 1.9 A$

Step by step solution

01

Part (a) Step 1: Given Information:

We have been given that

Capacitance ( $C$ )= $0.30 渭 F$

Peak voltage ( $E_{o}$ )= $10 V$

Emf frequency (n)= localid="1649958487243" $100 H z$

02

Part (a) Step 2: Solving:

Peak current I_ois given by : $I_{o} = E_{o} 脳蝇脳 C$

Putting the value of $(蝇) as 2 蟺 n$ in the above equation: $I_{o} = E_{o} 脳 2 蟺 n 脳 C$

Using the given values in the updated equation we get: $I_{o} = (10) 脳 2 蟺 (100) 脳 (0.30 脳 10^{- 6})$

There the peak value of current for a frequency of $100 H z$ is $I_{o} = 1.9 脳 10^{- 3} A$

03

Part (b) Step 1: Given Information:

We have been given that

Capacitance ( $C$ )= $0.30 u F$

Peak voltage ( $E_{o}$ )= $10 V$

Emf frequency (n)= $100 k H z$

04

Part (b) Step 2: Solving:

Using the expression of I_o that we earlier used: $I_{o} = E_{o} 脳 2 蟺 n 脳 C$

Putting the known values: $I_{o} = (10) 脳 2 蟺 (100 脳 10^{3}) 脳 (0.30 脳 10^{- 6})$

$I_{o} = 1.9 A$

Therefore the peak current value for an emf frequency of $100 k H z$ is $I_{o} = 1.9 A$

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Most popular questions from this chapter

A $200 惟$ resistor is connected to an AC source with ${鈭�}_{o} = 10 V$ . What is the peak current through the resistor if the emf frequency is (a) $100 H z$ ? (b) $100 k H z$ ?

II An electric circuit, whether it's a simple lightbulb or a complex amplifier, has two input terminals that are connected to the two output terminals of the voltage source. The impedance between the two input terminals (often a function of frequency) is the circuit's input impedance. Most circuits are designed to have a large input impedance. To see why, suppose you need to amplify the output of a high-pass filter that is constructed with a $1.2 k 惟$ resistor and a $15 渭 F$ capacitor. The amplifier you've chosen has a purely resistive input impedance. For a $60 Hz$ signal, what is the ratio $V_{R load} / V_{R no load}$ of the filter's peak voltage output with (load) and without (no load) the amplifier connected if the amplifier's input impedance is (a) $1.5 k 惟$ and (b) $150 k 惟$ ?

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.

A series RLC circuit consists of a $50 鈩�$ resistor, a localid="1650177582139" $3.3 m H$ inductor, and a localid="1650177586647" $480 n F$ capacitor. It is connected to an oscillator with a peak voltage of localid="1650177591401" $5.0 V$ . Determine the impedance, the peak current, and the phase angle at frequencies :

(a) localid="1650177630395" $3000 H z$ (b) localid="1650177635339" $4000 H z$ and (c) localid="1650177638990" $5000 H z .$

Figure P $32.47$ shows a parallel RC circuit.

a. Use a phasor-diagram analysis to find expressions for the peak currents $I_{R}$ and $I_{C}$ .

b. Complete the phasor analysis by finding an expression for the peak emf current I.

See all solutions

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