Final answer:
When the switch is closed, the voltage across the capacitor starts at 0 and gradually increases towards the voltage of the battery. The equation V = E(1 - e^-t/RC) can be used to calculate the voltage across the capacitor at any given time.
Step-by-step explanation:
When the switch is closed, the capacitor begins to charge. Since it is initially uncharged, the voltage across the capacitor is initially 0. However, as time goes on, the voltage across the capacitor increases and approaches the voltage of the battery.
The equation for voltage versus time when charging a capacitor through a resistor is given by V = E(1 - e-t/RC), where V is the voltage across the capacitor, E is the voltage of the battery, t is the time, R is the resistance, and C is the capacitance.
In this case, the voltage of the battery is given as 24 V and the capacitance is 1 μF. Therefore, the voltage across the capacitor after closing the switch can be calculated using the equation.