## RL Circuits

10.4 RL Circuits

### Learning Objectives

By the end of this section, you will be able to:

- Analyze circuits that have an inductor and resistor in series
- Describe how current and voltage exponentially grow or decay based on the initial conditions

### RL Circuits

**Practice!**

Practice 10.4.1 |
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Consider the circuit in the figure with S_{1} open and S_{2} at position a.Switch S _{1} is now thrown closed. At the instant it is closed, across which circuit element is the voltage equal to the emf of the battery? |

Practice 10.4.2 |
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Consider the circuit in the figure with S_{1} open and S_{2} at position a.After a very long time, across which circuit element is the voltage equal to the emf of the battery? |

**Discuss!**

Consider the circuit in the figure. Suppose the circuit elements have the following values: emf = 10.0 V, R = 6.50 Ω, and L = 34.0 mH.

(a) Calculate the current in the circuit after the switch has been closed for one time constant.

(b) Calculate the voltage across the resistor after one time constant has elapsed since the switch has been closed.

How long will it take after the switch is closed for the current to reach 99.0% of its steady-state value?