In Example 2 we discussed a simple electric circuit with resistance 12, inductance 4 H, and a

In Example 2 we discussed a simple electric circuit with resistance 12Ω, inductance 4 H, and a battery with voltage 60 V. If the switch is closed when t = 0, we modeled the current I at time t by the initial-value problem

Estimate the current in the circuit half a second after the switch is closed.

Data from Example 2

Suppose that in the simple circuit of Figure 9 the resistance is 12Ω, the inductance is 4 H, and a battery gives a constant voltage of 60 V.

Draw a direction field for Equation 1 with these values. 

What can you say about the limiting value of the current? 

Identify any equilibrium solutions. 

If the switch is closed when t = 0 so the current starts with I(0) = 0, use the direction field to sketch the solution curve.

Transcribed Image Text:

dI dt 15 - 31 I(0) = 0