A circuit consists of 3 components connected between 2 terminals: A 6 V source, a 90 Ω resistor and a 0.01 F capacitor. The capacitor is initially uncharged. The voltage source is turned on. What is the voltage across the capacitor after a very long time?
What is the current flowing through the above capacitor after a very long time?
To determine the voltage across the capacitor after a very long time, we need to understand the behavior of a capacitor in a DC circuit. When a DC voltage is applied to a capacitor, it charges up until it reaches the same voltage as the voltage source. However, it takes some time for the capacitor to fully charge.
In this case, the capacitor is initially uncharged, and a 6 V source is connected to it. Since the capacitor is uncharged, it will start charging up as soon as the voltage source is turned on. The charging process follows an exponential curve.
The time constant (τ) of the RC circuit, where R is the resistance and C is the capacitance, is given by the formula τ = RC. In this case, the resistor value is 90 Ω and the capacitance value is 0.01 F. So, the time constant is τ = (90 Ω)(0.01 F) = 0.9 seconds.
After a time equal to 5 times the time constant (5τ), the capacitor is considered fully charged. So, after a very long time, we can assume that the capacitor has reached its maximum charge and the voltage across it is equal to the voltage of the source, which is 6 V in this case. Therefore, the voltage across the capacitor after a very long time is 6 V.
Now, let's move on to the second question – the current flowing through the capacitor after a very long time. After the capacitor is fully charged, it acts as an open circuit, meaning no current flows through it in a DC circuit. Therefore, after a very long time, the current flowing through the capacitor is zero.