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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 potential difference of \(V=0.500 \mathrm{~V}\) is applied across a block of silicon with resistivity \(8.70 \cdot 10^{-4} \Omega \mathrm{m}\). As indicated in the figure, the dimensions of the silicon block are width \(a=2.00 \mathrm{~mm}\) and length \(L=15.0 \mathrm{~cm} .\) The resistance of the silicon block is \(50.0 \Omega\), and the density of charge carriers is \(1.23 \cdot 10^{23} \mathrm{~m}^{-3}\) Assume that the current density in the block is uniform and that current flows in silicon according to Ohm's Law. The total length of 0.500 -mm-diameter copper wire in the circuit is \(75.0 \mathrm{~cm},\) and the resistivity of copper is \(1.69 \cdot 10^{-8} \Omega \mathrm{m}\) a) What is the resistance, \(R_{w}\) of the copper wire? b) What are the direction and the magnitude of the electric current, \(i\), in the block? c) What is the thickness, \(b\), of the block? d) On average, how long does it take an electron to pass from one end of the block to the other? \(?\) e) How much power, \(P\), is dissipated by the block? f) In what form of energy does this dissipated power appear?

Two resistors with resistances \(R_{1}\) and \(R_{2}\) are connected in parallel. Demonstrate that, no matter what the actual values of \(R_{1}\) and \(R_{2}\) are, the equivalent resistance is always less than the smaller of the two resistances.

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