# 20.2 Ohm’s law: resistance and simple circuits

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## Making connections: conservation of energy

In a simple electrical circuit, the sole resistor converts energy supplied by the source into another form. Conservation of energy is evidenced here by the fact that all of the energy supplied by the source is converted to another form by the resistor alone. We will find that conservation of energy has other important applications in circuits and is a powerful tool in circuit analysis.

## Phet explorations: ohm's law

See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.

## Test prep for ap courses

If the voltage across a fixed resistance is doubled, what happens to the current?

1. It doubles.
2. It halves.
3. It stays the same.
4. The current cannot be determined.

(a)

The table below gives the voltages and currents recorded across a resistor.

 Voltage (V) 2.5 5 7.5 10 12.5 Current (A) 0.69 1.38 2.09 2.76 3.49
1. Plot the graph and comment on the shape.
2. Calculate the value of the resistor.

What is the resistance of a bulb if the current in it is 1.25 A when a 4 V voltage supply is connected to it? If the voltage supply is increased to 7 V, what will be the current in the bulb?

3.2 Ω, 2.19 A

## Section summary

• A simple circuit is one in which there is a single voltage source and a single resistance.
• One statement of Ohm's law gives the relationship between current $I$ , voltage $V$ , and resistance $R$ in a simple circuit to be $I=\frac{V}{R}.$
• Resistance has units of ohms ( $\text{Ω}$ ), related to volts and amperes by $1 \Omega =\text{1 V/A}$ .
• There is a voltage or $\text{IR}$ drop across a resistor, caused by the current flowing through it, given by $V=\text{IR}$ .

## Conceptual questions

The $\text{IR}$ drop across a resistor means that there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor? Explain.

How is the $\text{IR}$ drop in a resistor similar to the pressure drop in a fluid flowing through a pipe?

## Problems&Exercises

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is $3\text{.}\text{60 Ω}$ ?

0.833 A

Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows.

What is the effective resistance of a car's starter motor when 150 A flows through it as the car battery applies 11.0 V to the motor?

$7\text{.}\text{33}×{\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\Omega$

How many volts are supplied to operate an indicator light on a DVD player that has a resistance of $1\text{40}\phantom{\rule{0.25em}{0ex}}\Omega$ , given that 25.0 mA passes through it?

(a) Find the voltage drop in an extension cord having a $0\text{.}\text{0600-}\Omega$ resistance and through which 5.00 A is flowing. (b) A cheaper cord utilizes thinner wire and has a resistance of $0\text{.}\text{300}\phantom{\rule{0.25em}{0ex}}\Omega$ . What is the voltage drop in it when 5.00 A flows? (c) Why is the voltage to whatever appliance is being used reduced by this amount? What is the effect on the appliance?

(a) 0.300 V

(b) 1.50 V

(c) The voltage supplied to whatever appliance is being used is reduced because the total voltage drop from the wall to the final output of the appliance is fixed. Thus, if the voltage drop across the extension cord is large, the voltage drop across the appliance is significantly decreased, so the power output by the appliance can be significantly decreased, reducing the ability of the appliance to work properly.

A power transmission line is hung from metal towers with glass insulators having a resistance of $1\text{.}\text{00}×{\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\Omega .$ What current flows through the insulator if the voltage is 200 kV? (Some high-voltage lines are DC.)

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
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