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Chapter 25: Problem 63

A certain brand of hot dog cooker applies a potential difference of \(120 \mathrm{~V}\) to opposite ends of the hot dog and cooks it by means of the heat produced. If \(48 \mathrm{~kJ}\) is needed to cook each hot dog, what current is needed to cook three hot dogs simultaneously in \(2.0 \mathrm{~min}\) ? Assume a parallel connection.

Short Answer

Expert verified
Answer: The current needed to cook three hot dogs simultaneously in 2.0 minutes is 10 A.

Step by step solution

01

Convert time to seconds

Since we are given the time in minutes, we need to convert it into seconds for our calculations. We can do this by multiplying the given time by 60: 2.0 minutes * 60 seconds/minute = 120 seconds
02

Calculate the total energy needed

We know that 48 kJ of energy is needed to cook one hot dog, so to cook three hot dogs simultaneously, we need to multiply the energy required for one hot dog by three: 3 hot dogs * 48 kJ/hot dog = 144 kJ Now, convert the energy from kilojoules to joules: 144 kJ * 1000 J/kJ = 144000 J
03

Use the power formula to find the required power

We can use the formula for electrical power, P = E/t, where E is the total energy and t is the time taken. In this case, E = 144000 J and t = 120 seconds: P = 144000 J / 120 s = 1200 W
04

Calculate the current

Now that we have the required power (P), we can use the formula for electrical power to find the current (I). The formula is P = VI, where V is the potential difference and P is the power. We are given a potential difference of 120V: 1200 W = I * 120V Divide both sides by 120V to find the current (I): I = 1200 W / 120 V = 10 A So, a current of 10 A is needed to cook three hot dogs simultaneously in 2.0 minutes using the given hot dog cooker.

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Most popular questions from this chapter

A battery has a potential difference of \(14.50 \mathrm{~V}\) when it is not connected in a circuit. When a \(17.91-\Omega\) resistor is connected across the battery, the potential difference of the battery drops to \(12.68 \mathrm{~V}\). What is the internal resistance of the battery?

A potential difference of \(12.0 \mathrm{~V}\) is applied across a wire of cross-sectional area \(4.50 \mathrm{~mm}^{2}\) and length \(1000 . \mathrm{km} .\) The current passing through the wire is \(3.20 \cdot 10^{-3} \mathrm{~A}\). a) What is the resistance of the wire? b) What type of wire is this?

Why do light bulbs typically burn out just as they are turned on rather than while they are lit?

A current of \(0.123 \mathrm{~mA}\) flows in a silver wire whose cross-sectional area is \(0.923 \mathrm{~mm}^{2}\) a) Find the density of electrons in the wire, assuming that there is one conduction electron per silver atom. b) Find the current density in the wire assuming that the current is uniform. c) Find the electron's drift speed.

Which of the following is an incorrect statement? a) The currents through electronic devices connected in series are equal. b) The potential drops across electronic devices connected in parallel are equal. c) More current flows across the smaller resistance when two resistors are in parallel connection. d) More current flows across the smaller resistance when two resistors are in serial connection.
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