# Resistors in Circuits

## Problems

### practice

- Determine the following quantities for each of the two circuits shown below…
- the equivalent resistance,
- the total current from the power supply,
- the current through each resistor,
- the voltage drop across each resistor, and
- the power dissipated in each resistor.

- A kitchen in North America has three appliances connected to a 120 V circuit with a 15 A circuit breaker: an 850 W coffee maker, a 1200 W microwave oven, and a 900 W toaster.
- Draw a schematic diagram of this circuit.
- Which of these appliances can be operated simultaneously without tripping the circuit breaker?

- The diagram below shows a circuit with one battery and 10 resistors; 5 on the left and 5 on the right. Determine…
- the current through,
- the voltage drop across, and
- the power dissipated by each resistor.

- Given the circuit on the right…
- Calculate the equivalent resistance of the circuit.
- Calculate the current through the battery.
- Graph voltage as a function of location on the circuit assuming that
*V*_{a}= 0 V at the negative terminal of the battery. - Graph current as a function of location on the circuit.

### conceptual

- What happens to the total current as resistors are added to a circuit…
- in series?
- in parallel?

- State two reasons why household outlets are not wired together in series.
- What is meant by the term "short circuit"? What makes a short circuit dangerous?
- A power source and four identical, numbered light bulbs are connected together as shown in the circuit on the right.
- Rank the light bulbs in order of brightness.
- Describe the effect that removing any one of the light bulbs has (if any) on the brightness of the other three.
- remove bulb 1
- remove bulb 2
- remove bulb 3
- remove bulb 4

R _{1}R _{2}R _{3}R _{4}a. b. i. × b. ii. × b. iii. × b. iv. × - A power source and four identical, numbered light bulbs are connected together as shown in the circuit on the right.
- Rank the light bulbs in order of brightness.
- Describe the effect that removing any one of the light bulbs has (if any) on the brightness of the other three.
- remove bulb 1
- remove bulb 2
- remove bulb 3
- remove bulb 4

R _{1}R _{2}R _{3}R _{4}a. b. i. × b. ii. × b. iii. × b. iv. ×

### numerical

- Given the circuit on the right, find …
- the voltage drop across the 4 Ω resistor
- the voltage drop across the 5 Ω resistor
- the current through the 2 Ω resistor
- the current through the 7 Ω resistor

- Given the circuit on the right, determine…
- the equivalent resistance of the entire circuit
- the total current from the power supply
- the current through each resistor
- the voltage drop across each resistor

- Four identical resistors are combined in four different ways as shown in the diagram below. For the sake of convenience, let each have a resistance of 1 Ω. The + and − signs show the terminals of each combination.
- Which combination is strictly parallel? Determine its total resistance.
- Which combination is strictly series? Determine its total resistance.
- Which of the two combinations you analyzed in parts a. and b. has the lower resistance? Why does it have the lower resistance?
- Determine the equivalent resistance of the two remaining combinations.
- Which of the two combinations you analyzed in part d. has the lower resistance? Why does it have the lower resistance?

- The circuit shown on the right consists of eleven identical 1 Ω resistors connected to a 15 V power supply. Determine…
- the total resistance of the entire circuit
- the total current from the power supply
- the current through resistor
*R*_{1} - the current through resistor
*R*_{2} - the current through resistor
*R*_{3}

- Twelve identical 1 Ω resistors are connected into a circuit that consists of two square loops as show in the diagram on the right. Determine the resistance between the following pairs of points…
- b & g
- d & g
- f & g
- a & g
- a & h
- d & h
- g & h
- f & h

### investigative

- Track workers in the New York City subway system don't get their electricity from wall outlets. They use the third rail. Since the voltage of the third rail is different from the voltage of a wall outlet in an American home, they often use modified or specialized electrical devices. For example, the temporary lights the workers use are mounted on strips with five bulbs — never four, never six, always five. This design choice is intentional.
Source: MTA New York City Transit.

- What is the voltage of a typical household outlet in the United States?
- What is the voltage of the third rail in the New York City subway system?
- Why do the work lights used in the New York City subway come is strips with five light bulbs? Be sure to state the basic wiring pattern (series or parallel) in your answer.