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Chapter 31: 55P (page 938)

What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.60 A?

Short Answer

Expert verified

The value of the direct current is 1.84 A.

Step by step solution

01

Listing the given quantities:

The current, i=2.60A

02

Understanding the concepts of power dissipation:

Average power dissipated in resistance Rwhen the current isACand DC should be equated to find the direct current which will produce the same amount of thermal energy as an alternating current of 2.60 A

Formula:

Power Dissipation, Pd=id2R

03

 Step 3: Calculation of the value of the direct current:

Average power dissipated in resistance R when current is AC.

Pavg=irms2R

The power is dissipated in resistor R when current is DC.

Pd=id2R

Both these powers produce the same thermal energy. Hence,

Pavg=Pdirms2R=id2Rid=irms=i2

Substitute 2.60A for i in the above equation.

id=i2=2.62=1.84A

Hence, the value of the direct current is 1.84A.

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Most popular questions from this chapter

A series RLC circuit is driven in such a way that the maximum voltage across the inductor is 1.50timesthe maximum voltage across the capacitor andlocalid="1664189666110" 2timesthe maximum voltage across the resistor. (a) What is ϕfor the circuit? (b) Is the circuit inductive, capacitive, or in resonance? The resistance islocalid="1664189661326" 49.9ohm, and the current amplitude islocalid="1664189655682" 200mA. (c) What is the amplitude of the driving emf?

Figure 31-32 shows a driven RLC circuit that contains two identical capacitors and two switches. The emf amplitude is set at εm=12.0V, and the driving frequency is set at 60.0Hz. With both switches open, the current leads the emf by 30.9°. With switch S1closed and switch S2still open, the emf leads the current by 15.0°. With both switches closed, the current amplitude is 447mA. What are (a) R, (b) C , and (c) L?

An alternating emf source with a certain emf amplitude is connected, in turn, to a resistor, a capacitor, and then an inductor. Once connected to one of the devices, the driving frequency fdis varied and the amplitude Iof the resulting current through the device is measured and plotted. Which of the three plots in Fig. 31-22 corresponds to which of the three devices?

Curve a in Fig. 31-21 gives the impedance Z of a driven RC circuit versus the driving angular frequency ωd. The other two curves are similar but for different values of resistance R and capacitance C. Rank the three curves according to the corresponding value of R, greatest first.

In Fig. 31-33, a generator with an adjustable frequency of oscillation is connected to resistance R=100Ω, inductances L1=1.70mH and L2=2.30mH, and capacitances C1=4.00μF, C2=4.00μF , and C3=3.50μF . (a) What is the resonant frequency of the circuit? (Hint: See Problem 47 in Chapter 30.) What happens to the resonant frequency if (b) Ris increased, (c) L1is increased, and (d) C3 is removed from the circuit?
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