An LR-circuit is shown above with battery voltage VB, inductance L, and resistan

Question

An LR-circuit is shown above with battery voltage VB, inductance L, and resistance R. A generic form of any equations used would be much appreciated!

1. Describe the voltage in each component a very short time after the circuit is connected.
2. Describe the voltage in each component a long time after the circuit is connected.
3. Write a differential equation describing the circuit.
4. Solve the differential equation using the separation of variables method, showing your main steps.

An RC-circuit is shown above with battery voltage VB, capacitance C, and resistance R.
5. Describe the voltage in each component a very short time after the circuit is connected.
6. Describe the voltage in each component a long time after the circuit is connected.
7. Write a differential equation describing the circuit.
8. Solve the differential equation using the separation of variables method, showing your main steps.

Explanation / Answer

1.

a very short time after the circuit is connected , the inductor behaves as open circuit and all the voltage appear across the inductor resulting in zero current flowing through the circuit and resistor.

2.

after long time ,the circuit is connected, the inductor behaves as short circuit .the inductor offers no resistance and all the Voltage appears across the resistor.

3.

iR + L (di/dt) = V

5.

a very short time after the circuit is connected , the capacitor behaves as short circuit and all the voltage appear across the resistor .

6.

after long time ,the circuit is connected, the capacitr behaves as open circuit .and all the voltage appear across the capacitor resulting in zero current flowing through the circuit and resistor.

7.

R (di/dt) + i/C = 0

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