Question

the switch in (figure 1) has been open for a long time. it is closed at t = 0 s. what is the current through the battery immediately after the switch is closed?

Answer 1

Immediately after the switch is closed in a circuit with a battery, resistor, and an uncharged capacitor, the current through the battery is at its maximum, as defined by Ohm's law. The capacitor charges over time, causing the current to decrease exponentially until it reaches zero when full.

Step-by-step explanation:

When a switch in an electrical circuit containing a battery, a resistor, and an uncharged capacitor is closed, the behaviour of the current will depend on the state of the capacitor. Initially, at t = 0 s, since the capacitor is uncharged, it behaves like a short circuit, allowing the maximum current to flow through it. This initial current through the battery and resistor would be defined by Ohm's law, which is I(0) = ε/R where ε is the electromotive force (voltage) of the battery and R is the resistance of the resistor.

The current immediately after the switch is closed will then be the maximum possible current as the capacitor's resistance is initially zero and it doesn't oppose the flow of current. As time passes, the capacitor will start to charge, and the current through it will decrease exponentially until it reaches zero, when the capacitor is fully charged.

Answer 2

The initial current through the battery when the switch is closed in a circuit with a resistor and an initially uncharged capacitor is equal to the battery voltage divided by the total resistance. This current will decrease over time as the capacitor charges.

Step-by-step explanation:

When a switch is closed in an electric circuit containing a battery, a resistor, and an initially uncharged capacitor, at t = 0 s, the current through the battery will behave as if the capacitor is not present initially, because the uncharged capacitor acts like a short circuit. The initial current is therefore determined solely by the resistance in the circuit (Ohm's law), which is the voltage of the battery divided by the total resistance.

The immediate current through the battery when the switch is closed can be calculated using I(0) = ε/R, where ε represents the electromotive force (voltage) of the battery and R is the total resistance in the circuit. As time progresses, the capacitor will start to charge and the current will exponentially decrease until it reaches zero once the capacitor is fully charged.