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Chapter 32: Q. 38 (page 925)

A series RLC circuit attached to a 120V/60Hzpower line draws a 2.4Arms current with a power factor of 0.87. What is the value of the resistor?

Short Answer

Expert verified

The value of resistor is43.5Ω.

Step by step solution

01

Given Information

We are given that rms current I=2.4A,Voltage is V=120Vand power factor is Pf=0.87

and we have to find out the value of resistor.

02

Formula Used

Now, using the formula,

We get P=(V)(I)(Pf)

where V is voltage, I is current and Pfis the power factor.

Putting the value of variables in equation,

We get,

P=(120)(2.4)(0.87)=250.56W

03

Simplify

Now, using the formula

P=I2R,

where P is power, I is current and R is resistor,

Putting all the variable in equation we get,

250.56=(2.4)2R

On solving,

we get

R=43.5Ω

The value of resistor is43.5Ω.

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Most popular questions from this chapter

The current lags the emf by 30° in a series RLC circuit with E0=10V and R=50Ω. What is the peak current through the circuit?

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf E=E0cosvt, three separate wires carry currents for the emfs E1=E0cosvt,E2=E0cos1vt+120°,andE3=E0cos1vt-120°. This is why the long-distance transmission lines you see in the countryside have three parallel wires, as do many distribution lines within a city.

a. Draw a phasor diagram showing phasors for all three phases of a three-phase emf.

b. Show that the sum of the three phases is zero, producing what is referred to as neutral. In single-phase electricity, provided by the familiar electric outlets in your home, one side of the outlet is neutral, as established at a nearby electrical substation. The other, called the hot side, is one of the three phases. (The round opening is connected to ground.)

c. Show that the potential difference between any two of the phases has the rms value where is the familiar single-phase rms voltage. Evaluate this potential difference for . Some high-power home appliances, especially electric clothes dryers and hot-water heaters, are designed to operate between two of the phases rather than between one phase and neutral. Heavy-duty industrial motors are designed to operate from all three phases, but full three-phase power is rare in residential or office use.

A television channel is assigned the frequency range from 54mHZto 60mHZ. A series RLC tuning circuit in a TV receiver resonates in the middle of this frequency range. The circuit uses a 16pFcapacitor.

a. What is the value of the inductor?

b. In order to function properly, the current throughout the frequency range must be at least 50% of the current at the resonance frequency. What is the minimum possible value of the circuit’s resistance?

A motor attached to a 120V/60HZpower line draws an 8Acurrent. Its average energy dissipation is 800W.

a. What is the power factor?

b. What is the rms resistor voltage?

c. What is the motor’s resistance?

d. How much series capacitance needs to be added to increase the power factor to 1?

The resonance frequency of a series RLC circuit is less than the EMF frequency. Does the current lead or lag the EMF? Explain.
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