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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, $i = 2.60 A$

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, $P_{d} = i_{d}^{2} R$

03

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

Average power dissipated in resistance R when current is AC.

$P_{avg} = i_{rms}^{2} R$

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

$P_{d} = i_{d}^{2} R$

Both these powers produce the same thermal energy. Hence,

$\begin{array}{rcl} P_{avg} & = & P_{d} \\ i_{rms}^{2} R & = & i_{d}^{2} R \\ i_{d} & = & i_{rms} \\ = & \frac{i}{\sqrt{2}} \end{array}$

Substitute 2.60A for i in the above equation.

$\begin{array}{rcl} i_{d} & = & \frac{i}{\sqrt{2}} \\ = & \frac{2.6}{\sqrt{2}} \\ = & 1.84 A \end{array}$

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

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Most popular questions from this chapter

An ac generator has emf $蔚 = 蔚_{m} s i n 蝇_{d} t$ , with $蔚_{m} = 25.0 V$ and $蝇_{d} = 377 \frac{rad}{s}$ . It is connected to an $L = 12.7 H$ inductor. (a) What is the maximum value of the current? (b) When the current is a maximum, what is the emf of the generator? (c) When the emf of the generator isrole="math" localid="1663220843017" $- 12.5 V$ and increasing in magnitude, what is the current?

The frequency of oscillation of a certain LCcircuit is $200 kHz$ . At time $t = 0$ , plate Aof the capacitor has maximum positive charge. At what earliest time $t > 0$ will

(a) plate Aagain have maximum positive charge,(b) the other plate of the capacitor have maximum positive charge, and (c) the inductor have maximum magnetic field?

Does the phasor diagram of Fig. 31-26 correspond to an alternating emf source connected to a resistor, a capacitor, or an inductor? (b) If the angular speed of the phasors is increased, does the length of the current phasor increase or decrease when the scale of the diagram is maintained?

LCoscillators have been used in circuits connected to loudspeakers to create some of the sounds of electronic music. What inductance must be used with a 6.7 碌F capacitor to produce a frequency of10 kHz, which is near the middle of the audible range of frequencies?

An ac generator with emf amplitude $蔚_{m} = 220 V$ and operating at frequency $f_{d} = 400 Hz$ causes oscillations in a series $R L C$ circuit having $R = 220 惟$ , $L = 150 mH$ , and $C =24.0 渭贵$ . Find (a) the capacitive reactance $X_{C}$ , (b) the impedance Z, and (c) the current amplitude I. A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of (d) $X_{C}$ , (e) Z, and (f) Iincrease, decrease, or remain the same.

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