1- What is the impedance of a 1.34 k? resistor, a 105 mH inductor, and a 24.7 ?F

Question

1- What is the impedance of a 1.34 k? resistor, a 105 mH inductor, and a 24.7 ?F capacitor

A) 1340 ? B)1340 Hz C) 990 ? D) 2350 ?

2- When an ac generator with a frequency of 160 Hz and an rms voltage of 34 V is connected to an RC circuit, the rms current is 0.28 A.If the resistance has a value of 72 ?, what is the value of the capacitance?

A) 5.0×10 ?5 F B)1.0×10 ?5 F C) 100 F D) 2.3x10 -6 F

3- Consider an RLC circuit with R = 105 ? , L = 503 mH , and C = 0.210 ?F. At what frequency is this circuit in resonance?

A) 650 Hz B) 400 Hz C) 345 Hz D) 490 Hz E) 745 Hz

4- An ac generator with a frequency of 25.0 Hz and an rms voltage of 13.0 V is connected to a 58.0 ?F capacitor. What is the maximum current in this circuit?

A) 0.0167 A B) 1.67 A C) 0.167 A D) 2.5 A

5- A cell phone transmits at a frequency of 2.04×10 8 Hz . What is the wavelength of the electromagnetic wave used by this phone?

A) 2.3 m B)1.47 m C) 1.67 m D) 3.2 m

Explanation / Answer

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1.

Inductive reactance

XL=2pifL=2pi*60*0.105 =39.584 ohms

Capacitive reactance

XC=1/2pifC=1/2pi*60*(24.7*10-6) =107.392 ohms

Impedance

Z=sqrt[R2+(XL-XC)2]

Z=sqrt[13402+(39.584-107.392)2]

Z=1341.7 ohms =1340 ohms (approx)

2.

Impedance

Z=V/I =34/0.28

Z=121.428 ohms

Capacitive reactance

XC=sqrt[Z2-R2]=sqrt[121.4282-722]=97.78 ohms

Capacitance

C=1/2pifXC =1/2pi*160*97.78

C=1*10-5 F

3.

Resonant frequency

f=1/2pisqrt(LC) =1/2pisqrt(0.503*0.21*10-6)

f=490 Hz

4.

Capacitive reactance

XC=1/2pifC=1/2pi*25*(58*10-6)=109.762 ohms

Rms Current

Irms=13/109.762 =0.1184 A

Peak current

IP=sqrt(2)*0.1184 =0.167 A

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