4.8mF capacitor in series with 500 ohm resistor is connected, via a switch, to a 12V battery. What is the current through the resistor at t=1.0s after the switch is closed?
I tried doing I^2R = 1/2 CV^2 and solving for I but the answer wasn't correct.
can some1 please help? thanks.
the correct answer is 16mA.
Current varies with time as the capacitor charges up. This is a transient circuit problem that needs to be solved with a differential equation. The solution is
I = (V/R)[1 - e^(-t/(RC))]
V/R = 24 mA
RC = 2.4 seconds
t/RC = 0.4167
e^(-0.4167) = 0.659
I = 24*.659 = 15.8 mA
They have rounded it off to two significant figures, to get 16 mA. That is what should be done, since 12V has only two sig. figures.
I don't know why you used the power in the reisistor is equal to the energy in the capacitor.
I=12/R * e^-t/RC
Bob's formula is correct. Forget the "1 - " in my answer
I = (V/R) * e^-t/RC
That is the one I used to do the calculation anyway
To find the current through the resistor at t=1.0s, you can use the formula for the charging or discharging of an RC circuit.
In this case, the capacitor is being charged, so we use the charging formula:
Vc(t) = V(1 - e^(-t/RC))
Where:
Vc(t) is the voltage across the capacitor at time t,
V is the supply voltage (12V in this case),
t is the time since the switch was closed (1.0s in this case),
R is the resistance in the circuit (500 ohms in this case), and
C is the capacitance (4.8mF = 0.0048F in this case).
To find the current through the resistor, we can use Ohm's Law:
I = Vc(t) / R
Substituting the values we have:
Vc(1.0s) = 12(1 - e^(-1.0/(500 * 0.0048)))
I = Vc(1.0s) / 500
Now let's calculate it step by step:
1. Calculate the exponential term e^(-1.0/(500 * 0.0048)). This gives us e^(-0.4167) ≈ 0.6585.
2. Calculate Vc(1.0s) = 12(1-0.6585) ≈ 4.1305V.
3. Finally, calculate I = 4.1305V / 500 ≈ 0.00826A ≈ 8.26mA.
So, the current through the resistor at t=1.0s is approximately 8.26mA.
It seems the correct answer you provided (16mA) may be incorrect or it might be referring to a different scenario.