In: Physics
Consider a RC circuit. At time t=0, the circuit is closed. ( a) Draw how the current behaves with time. (b) What about the power dissipated by the resistor ? (also draw it as a function of t)
Kirchhoff’s Loop Rule
At t=0, there is no charge on (hence no potential across) the capacitor so at the “instant” the switch is closed, we expect a current of I0=ε/R (voltage drop is only across the resistor). As the capacitor charges, we expect the current to fall.
Close Switch at t=0
Charge will flow on the capacitor and the current will decrease until we reach i = 0, then:
the final value charge, Qf does not depend on R
This is a differential equation. We can rearrange and integrate to find what we need.
Taking the exponents (inverse log) both sides
Taking the time derivative, to get the instantaneous , current, i
Solution(B)
Kirchhoff’s Loop Rule
At t=0, there is no charge on (hence no potential across) the capacitor so at the “instant” the switch is closed, we expect a current of I0=ε/R (voltage drop is only across the resistor). As the capacitor charges, we expect the current to fall.
Close Switch at t=0
Charge will flow on the capacitor and the current will decrease until we reach i = 0, then:
the final value charge, Qf does not depend on R
This is a differential equation. We can rearrange and integrate to find what we need.
Taking the exponents (inverse log) both sides
Taking the time derivative, to get the instantaneous , current, i
Solution(B)