**Resistors in Series**

All resistors are connected end to end. Recall the river analogy: current is analogous to a river of water, but instead of water flowing, charge does. With resistors in series, there is only one river, so there is only one current. But since there is a voltage drop across each resistor, they may all have different voltages across them. The more resistors in series the more rocks in the river, so the less current that flows.

#### Example

A circuit is wired up with two resistors in series.

Both resistors are in the same ‘river’, so both have the same current flowing through them. Neither resistor has a direct connection to the power supply so neither has 20V across it. But the combined voltages across the individual resistors add up to 20V.

What is the total resistance of the circuit?

The total resistance is

What is the total current coming out of the power supply?

Use Ohm’s Law

How much power does the power supply dissipate?

How much power does each resistor dissipate?

Each resistor has different voltage across it, but the same current. So, using Ohm’s law, convert the power formula into a form that does not depend on voltage.

How much voltage is there across each resistor?

In order to calculate voltage across a resistor, use Ohm’s law.

### Simulation

### Review

- Regarding the circuit below.
- If the ammeter reads
2A , what is the voltage? - How many watts is the power supply supplying?
- How many watts are dissipated in each resistor?

- If the ammeter reads
- Five resistors are wired in series. Their values are
10Ω ,56Ω ,82Ω ,120Ω and180Ω .- If these resistors are connected to a 6 V battery, what is the current flowing out of the battery?
- If these resistors are connected to a 120 V power supply, what is the current flowing out of the battery?
- In order to increase current in your circuit, which two resistors would you remove?

- Given the resistors above and a 12 V battery, how could you make a circuit that draws 0.0594 A?

### Review (Answers)

- a.
224V b.448W c.400W by100 Ω and48W by12 Ω - a. 0.013 A b. 0.27 A c.
120Ω and180Ω - Need about
202Ω of total resistance. So if you wire up the120Ω and the82Ω in series, you'll have it.