1)A resistor with resistance R and a capacitor with capacitance C are connected

Question

1)A resistor with resistance R and a capacitor with capacitance C are connected in series to an AC voltage source. The time-dependent voltage across the capacitor is given by VC(t)=VC0sint.

If R=3k, C=100pF, VC0=100mV, and =105rad/s, what is VR?

2)You want the current amplitude through a inductor with an inductance of 4.10 mH (part of the circuitry for a radio receiver) to be 2.70 mA when a sinusoidal voltage with an amplitude of 12.0 V is applied across the inductor.

What frequency is required?

3)In an L-R-C series circuit, the source has a voltage amplitude of 120 V , R = 85.0 , and the reactance of the capacitor is 483 . The voltage amplitude across the capacitor is 364 V .

What two values can the reactance of the inductor have?

Explanation / Answer

2)

current amplitude I = VL/(XL) =

VL - voltage amplitude

XL = inductive reactance = w*L = 2*pi*f*L

I = VL/(2*pi*f*L)

f = VL/(2*pi*I*L)

f = 12/(2*pi*2.7*10^-3*4.1*10^-3) = 172526 Hz

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(3)

given voltage amplitude V = 120

Xc = 483 ohm

R = 85 ohm

Vc = 364 = I*Xc

I = Vc/Xc = 364/483 = 0.754 A

impedance Z = V/I = 120/0.754 = 159.1 ohms

XL = ?

therefore from relation

Z = sqrt(R^2+(XL-Xc)^2)

159.1 = sqrt(85^2 + (XL-483)^2)

XL = 348.5 ohms or 617.4 ohms <<<<------answer

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