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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 by an alternating source at a frequency of400Hz and an emf amplitude of 90.0V. The resistance is20.0Ω, the capacitance is12.1μF, and the inductance is24.2mH. What is the RMS potential difference across (a) the resistor, (b) the capacitor, and (c) the inductor? (d) What is the average rate at which energy is dissipated?

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?

The energy in an oscillating LCcircuit containing an1.25Hinductor is5.70μJ. The maximum charge on the capacitor is175μC. For a mechanical system with the same period, (a)Find the mass. (b) Find the spring constant. (c) Find the maximum displacement. (d) Find the maximum speed.

Figure 31-36 shows an ac generator connected to a “black box” through a pair of terminals. The box contains an RLC circuit, possibly even a multiloop circuit, whose elements and connections we do not know. Measurements outside the box reveal thatε(t)=(75.0V)sin(ωdt)and i(t)=(1.20A)sin(ωdt+42.0°).

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?
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