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Chapter 7: Problem 24

A simple electric circuit consists of a constant-voltage power supply and a variable resistor. What effect does reducing the resistance have on the current in the circuit and on the power output of the power supply?

Short Answer

Expert verified
Answer: When the resistance is reduced in a simple electric circuit with a constant-voltage power supply, the current flowing through the circuit increases, and consequently, the power output of the power supply also increases.

Step by step solution

01

Understand the given parameters

In a simple electric circuit, a constant-voltage power supply is connected to a variable resistor. Reducing the resistance will affect the current and power output in the circuit.
02

Recall Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. Mathematically, Ohm's Law is represented as: I = \frac{V}{R}
03

Analyze the effect on current

Now, let's analyze the effect of reducing the resistance (R) on the current (I) in the circuit. From Ohm's Law, we know that current is inversely proportional to resistance. So, when the resistance decreases, the current will increase.
04

Recall the formula for electrical power

The electrical power (P) in a circuit can be calculated using the formula: P = IV Where I is the current, and V is the voltage across the two points.
05

Analyze the effect on power output

We identified in Step 3 that reducing the resistance increases the current. Now, we will use the power formula to analyze the effect on power output. Since the voltage (V) remains constant in this circuit, an increase in current (I) will result in an increase in power (P). Therefore, reducing the resistance will increase the power output of the power supply. In conclusion, reducing the resistance in a simple electric circuit with a constant-voltage power supply will increase the current flowing through the circuit and also increase the power output of the power supply.

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