How to calculate the potential energy in a CR circuit with a resistor and 10micro-farrad capacitor before the switch is closed. the capacitor has a charge of 100 v and two seconds after the switch is closed looses 37% of its original value.
To calculate the potential energy in a CR circuit (capacitor and resistor), we need to understand the concept of potential energy stored in a capacitor and the behavior of the capacitor when the switch is closed.
1. Calculate the initial potential energy (U0) stored in the capacitor:
- Use the formula U = 0.5 * C * V^2, where U is the potential energy, C is the capacitance, and V is the initial voltage across the capacitor.
- In this case, the capacitance (C) is given as 10 microfarads (10μF) and the initial voltage (V) is given as 100 volts (100V).
- Substitute these values into the formula: U0 = 0.5 * 10 * 10^-6 * (100)^2.
2. Calculate the final potential energy (Uf) stored in the capacitor:
- Given that the capacitor loses 37% of its original charge, we can assume it loses 37% of its original voltage as well.
- Calculate the final voltage (Vf) by subtracting 37% of the original voltage from the initial voltage: Vf = V - (0.37 * V).
- Substitute the values into the formula: Uf = 0.5 * 10 * 10^-6 * (Vf)^2.
3. Calculate the percentage of potential energy remaining:
- Calculate the percentage remaining by dividing the final potential energy (Uf) by the initial potential energy (U0) and multiply by 100: Remaining % = (Uf / U0) * 100.
Note: To find the specific values, you need to evaluate the above equations by substituting the given values into them.