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What power is supplied to the starter motor of a large truck that draws \(250 \mathrm{~A}\) of current from a \(24.0 \mathrm{~V}\) battery hookup?

Short Answer

Expert verified
The power supplied to the starter motor is 6000 watts (or 6 kW).

Step by step solution

01

Understanding Power

Power in an electrical circuit is calculated by the formula P = IV, where P is the power in watts, I is the current in amperes, and V is the voltage in volts.
02

Applying the Power Formula

Substitute the given values into the power formula. In this case, I = 250 A and V = 24.0 V.
03

Calculating the Power

Perform the multiplication to find the power P: P = 250 A * 24.0 V.
04

Performing the Multiplication

Multiply the current by the voltage to get the power in watts: P = 6000 W.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Power Formula
The power formula is fundamental for understanding how electrical energy is used or generated in a circuit. Power, denoted as P, is the rate at which electrical energy is converted to another form of energy, like mechanical or heat energy. The formula to calculate power is straightforward: it's the product of electric current (I) and voltage (V), succinctly expressed as \( P = IV \).

When you look at the exercise provided, where a truck's starter motor draws current from a battery, we apply this exact formula. By substituting the given values of current and voltage into \( P = IV \) and performing a simple multiplication, we can calculate the power in watts that the starter motor uses, which is vital for assessing the truck's electrical system performance.
Electric Current
Electric current, symbolized by the capital letter I, is a flow of electric charge, measured in amperes (A). It's an essential component of the power formula and represents the rate at which charge passes through a point in a circuit. A higher current means more charge is moving through and thus potentially more power if the voltage stays the same.

Think of it like a river: the amount of water flowing past a point can be considered analogous to the current. In our truck starter motor example, a current of 250 A flows from the battery. This high current is typical of starter motors which require significant 'force' to crank an engine.
Voltage
Voltage, denoted as V and measured in volts, is the pressure from an electrical circuit's power source that pushes charged electrons through a conducting loop, enabling them to do work, such as lighting a bulb or turning a motor. It can also be thought of as the electric potential difference between two points in a circuit.

Returning to our river analogy, voltage is similar to the water pressure in a hose. In the textbook exercise, the voltage available from the truck's battery is 24.0 V, which pushes the current through the motor, enabling it to start the truck's engine.
Watts
A watt, symbolized by W, is the unit of power in the International System of Units (SI). It quantifies the rate of energy transfer. One watt is defined as one joule of energy transferred per second. In terms of electrical systems, when we talk about watts, we're discussing how much energy the system is using or producing at any given moment.

In the context of the exercise, once you have multiplied the current by the voltage, you determine that the starter motor draws 6,000 W from the battery. This power output is substantial and demonstrates how much energy is needed to start a large truck's engine. The concept of watts translates this energy requirement into a language that engineers and technicians can use to design and troubleshoot electrical systems.

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Most popular questions from this chapter

(a) What is the internal resistance of a voltage source if its terminal voltage drops by \(2.00 \mathrm{~V}\) when the current supplied increases by \(5.00 \mathrm{~A} ?\) (b) Can the emf of the voltage source be found with the information supplied?

A person with body resistance between his hands of \(10.0 \mathrm{k} \Omega\) accidentally grasps the terminals of a 20.0\(\mathrm{kV}\) power supply. (Do NOT do this!) (a) Draw a circuit diagram to represent the situation. (b) If the internal resistance of the power supply is \(2000 \Omega\), what is the current through his body? (c) What is the power dissipated in his body? (d) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in this situation to be \(1.00 \mathrm{~mA}\) or less? (e) Will this modification compromise the effectiveness of the power supply for driving low-resistance devices? Explain your reasoning.

Electron guns are used in X-ray tubes. The electrons are accelerated through a relatively large voltage and directed onto a metal target, producing X-rays. (a) How many electrons per second strike the target if the current is \(0.500 \mathrm{~mA} ?\) (b) What charge strikes the target in \(0.750 \mathrm{~s}\) ?

What is the output voltage of a \(3.0000-\mathrm{V}\) lithium cell in a digital wristwatch that draws \(0.300 \mathrm{~mA}\), if the cell's internal resistance is \(2.00 \Omega ?\)

(a) What is the internal resistance of a \(1.54-\mathrm{V}\) dry cell that supplies \(1.00 \mathrm{~W}\) of power to a \(15.0-\Omega\) bulb? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

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