# Differential Equations - Elementary Application

Electric Circuits

An RL circuit has the following values: R=550 ohms, L=4 henrys and Esub0=110 volts. If i(0)= 0 in the circuit, when does the current reach 90% of its limiting value?

### Using the formula: E = Ri +

Using the formula: E = Ri + Ldi/dt

I integrate it and got:
Et = Rit + Li + E0

When i(0)=0, substituting to the equation..
E=0

The equation will be then:
E0= -Rit - Li

Subsituting values:
R= 550 , L=4 , E0=110
I got
110= -550it - 4i
110= -i (550t-4)
i= -110 / ( 550t -4)

What should I do with this information then?

The problem states that the other i is 90% of the limiting value. How can I solve for the limiting value?

### 3. A resistance of 100 kΩ is

3. A resistance of 100 kΩ is connected in series with a 100 μF capacitor. If the combination is suddenly connected across a 125 V dc source. Determine the current one second after the switch is closed.

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