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Chapter 21: Problem 6

A 4.0 -k \(W\) heater is designed to be connected to a \(120-V\) ms source. What is the power dissipated by the heater if it is instead connected to a \(120-\mathrm{V}\) de source?

Short Answer

Expert verified
Answer: The power dissipated by the heater when connected to a 120 V DC source is 4000 W, or 4 kW.

Step by step solution

01

Calculate the resistance of the heater

To find the resistance of the heater, we can use the formula for power in terms of voltage and resistance: \(P = \frac{V^2}{R}\). Rearrange this formula for resistance, \(R = \frac{V^2}{P}\). We know the power provided by the heater is 4 kW, or 4000 W, and the RMS voltage is 120 V. So we have: \(R = \frac{(120 V)^2}{4000 W}\) Calculating the resistance: \(R = \frac{14400 V^2}{4000 W} = 3.6 \,\Omega\)
02

Calculate the power dissipated by the heater using DC source

Now we have the resistance of the heater, and we are given a 120 V DC source. We can calculate the power dissipated by the heater using the same power formula, \(P = \frac{V^2}{R}\). Plug in the DC voltage of 120 V and the resistance of 3.6 Ohms: \(P = \frac{(120 V)^2}{3.6 \,\Omega}\) Calculating the power: \(P = \frac{14400 V^2}{3.6 \,\Omega} = 4000 W\) Thus, the power dissipated by the heater when connected to a 120 V DC source is 4000 W, or 4 kW.

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Most popular questions from this chapter

A capacitor to be used in a radio is to have a reactance of \(6.20 \Omega\) at a frequency of \(520 \mathrm{Hz}\). What is the capacitance?
An RLC series circuit has \(L=0.300 \mathrm{H}\) and \(C=6.00 \mu \mathrm{F}\) The source has a peak voltage of \(440 \mathrm{V}\). (a) What is the angular resonant frequency? (b) When the source is set at the resonant frequency, the peak current in the circuit is \(0.560 \mathrm{A}\). What is the resistance in the circuit? (c) What are the peak voltages across the resistor, the inductor, and the capacitor at the resonant frequency?
In an RLC series circuit, these three elements are connected in scries: a resistor of \(60.0 \Omega,\) a 40.0 -mH inductor, and a \(0.0500-\mathrm{F}\) capacitor. The series elements are connected across the terminals of an ac oscillator with an rms voltage of \(10.0 \mathrm{V}\). Find the resonant frequency for the circuit.
In an RLC circuit, these three clements are connected in series: a resistor of \(20.0 \Omega,\) a \(35.0-\mathrm{mH}\) inductor, and a 50.0 - \(\mu\) F capacitor. The ac source of the circuit has an rms voltage of \(100.0 \mathrm{V}\) and an angular frequency of $1.0 \times 10^{3} \mathrm{rad} / \mathrm{s} .$ Find (a) the reactances of the capacitor and inductor, (b) the impedance, (c) the rms current, (d) the current amplitude, (e) the phase angle, and (f) the rims voltages across each of the circuit elements. (g) Does the current lead or lag the voltage? (h) Draw a phasor diagram.
At what frequency is the reactance of a 6.0 - \(\mu\) F capacitor equal to $1.0 \mathrm{k} \Omega ?$
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