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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

The circuit shown has a source voltage of \(440 \mathrm{V}\) ms, resistance \(R=250 \Omega\), inductance \(L=0.800 \mathrm{H},\) and capacitance $C=2.22 \mu \mathrm{F} .\( (a) Find the angular frequency \)\omega_{0}$ for resonance in this circuit. (b) Draw a phasor diagram for the circuit at resonance. (c) Find these rms voltages measured between various points in the circuit: \(V_{a b}, V_{b c}, V_{c d}, V_{b d},\) and \(V_{c d},\) (d) The resistor is replaced with one of \(R=125 \Omega\). Now what is the angular frequency for resonance? (e) What is the rms current in the circuit operated at resonance with the new resistor?
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A generator supplies an average power of \(12 \mathrm{MW}\) through a transmission line that has a resistance of \(10.0 \Omega .\) What is the power loss in the transmission line if the rms line voltage \(8_{\text {rms }}\) is (a) \(15 \mathrm{kV}\) and (b) \(110 \mathrm{kV} ?\) What percentage of the total power supplied by the generator is lost in the transmission line in each case? (IMAGE CAN'T COPY)
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.
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