RC Circuits Need help Please show calculations Derive the eq

RC Circuits. Need help. Please show calculations:

Derive the equation required in the calculations to determine C. Do your calculated values of C depend on the exact value of the emf. epsilon. of the battery used? Explain. FIG. 20: Resistor-capacitor circuit. Consider the circuit in the figure with R = r = 200 l Ohm, epsilon = 10 Volt, and C = 100 mu F. When the switch has been closed for a long time, what current would you expect to be drawn from the battery? How much charge is there on the capacitor? When the switch is first closed, what current would you expect to be drawn from the battery?

Solution

1. capacitance of capacitor does not depends on emf of battery,

value of C is fixed.

2. No

3. after long time,

capacitor will be fully charged and no current wil flow from capacitor.

hence current through battery, I = e / (R + r)

I = 10 / (200000 + 200000) = 2.5 x 10^-5 A, Or 0.025 mA

4. PD across capacitor = e-Ir = 10 - (200 x 10^3 x 2.5 x 10^-5)

= 5 volt

Q = CV = 100uF x 5 = 500 uC

5. when first swicthed is closed then capacitor will behave like plain wire.(no resistance)
hence R will short circuited and no current will flow through R.

hence current through battery, I = e/r = 5 x 10^-5 A or 0.05 mA