In this worksheet, we will practice calculating the current produced by voltage sources with internal resistance when connected to external resistances.

**Q2: **

A child’s electronic toy is supplied by three 1.58-V alkaline cells, in series with a 1.53-V carbon-zinc dry cell. The cells supply power to a load of resistance 10.0 Ω. The alkaline cells have internal resistances of 0.0200 Ω and the dry cell has a 0.100 Ω internal resistance.

What is the total current in the toy?

How much power is supplied to the load?

What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?

**Q3: **

Consider the circuit shown. Each battery has an emf of 1.50 V and an internal resistance of 1.00 Ω.

What is the current through the external resistor, which has a resistance of 10.00 ohms?

What is the terminal voltage of each battery?

**Q4: **

A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A.

What is the battery’s internal resistance?

What power is dissipated inside the battery?

At what rate will the temperature of the battery increase if its mass is 20.0 kg and it has a specific heat capacity of ? Assume that the battery is perfectly insulated.

**Q5: **

A resistor rated at 250 kΩ is connected across two D cell batteries (each 1.50 V) in series, with a total voltage of 3.00 V. The manufacturer advertises that their resistors are within of the rated value.

What is the maximum possible current through the resistor?

What is the minimum possible current through the resistor?

**Q6: **

The label on a 3.20-Ω-resistance battery-powered radio recommends the use of rechargeable 1.25-V-emf nickel-cadmium cells, rather than 1.58-V-emf alkaline cells.

Nickel-cadmium cells have an internal resistance of 0.0400 Ω. How much power does one of these cells supply to the radio?

Alkaline cells have an internal resistance of 0.200 Ω. How much power does one of these cells supply to the radio?

**Q7: **

A battery of emf 6.00 V has an internal resistance of 0.0833 Ω.

What current would be produced if the battery terminals were momentarily shorted together by a connector with negligible resistance?

The battery is connected to a circuit and produces a 0.250 A current. What is the battery’s terminal voltage?

**Q8: **

The terminal voltage of a 3.60 V emf cell with an internal resistance of 0.250 Ω is measured by placing a 4.00 kΩ voltmeter across the battery’s terminals, as shown in the accompanying diagram.

What is the current in the voltmeter?

- A A
- B A
- C A
- D A
- E A

What is the terminal voltage of the battery?

What is the ratio of the terminal voltage of the battery to its emf?

- A
- B
- C
- D
- E

**Q9: **

An automobile starter motor has an equivalent resistance of 0.0700 Ω and is supplied by a battery with a terminal voltage of 15.0 V that has a 0.0200 Ω internal resistance.

What is the current supplied to the motor?

What is the emf applied on the battery?

What power is supplied to the motor by the battery?

**Q10: **

A car battery with an 18.0 V emf and an internal resistance of 0.0900 Ω is being charged with a current of 70.0 A.

What is the terminal voltage of the battery?

At what rate is energy being dissipated in the battery?