# Current and voltage with inductors and capacitors

• Cocoleia
In summary, in inductors, current is directly proportional to the rate of change of magnetic flux while voltage is inversely proportional to the rate of change of current. In capacitors, current is directly proportional to the rate of change of voltage while voltage is inversely proportional to the rate of change of charge. Inductors and capacitors both impede the flow of current by storing energy, causing a delay in current flow through the circuit. The relationship between inductance and current is described by Faraday's Law of Induction. The voltage across a capacitor changes over time as it charges and discharges. The time constant of an RC or RL circuit determines how quickly the circuit will reach a steady state after a change in current or
Cocoleia

## Homework Statement

I am given the following circuit:

and asked to solve for v(t) and i(t)

## The Attempt at a Solution

If this is right, I don't know where to go from here.

Check the signs in your R||C calculation.

One place you can go from there is to find the current from the source, hence the current through the inductor. You could then determine the voltage across the inductor due to that current. Then you're on your own to use that knowledge to proceed further.

## 1. What is the difference between current and voltage in inductors and capacitors?

In inductors, current is directly proportional to the rate of change of magnetic flux, while voltage is inversely proportional to the rate of change of current. In capacitors, current is directly proportional to the rate of change of voltage, while voltage is inversely proportional to the rate of change of charge.

## 2. How do inductors and capacitors affect the flow of current in a circuit?

Inductors impede the flow of current by storing energy in a magnetic field, while capacitors impede the flow of current by storing energy in an electric field. Both components can also store and release energy, causing a delay in current flow through the circuit.

## 3. What is the relationship between inductance and current in an inductor?

The relationship between inductance and current is described by Faraday's Law of Induction, which states that the induced electromotive force (voltage) in an inductor is equal to the rate of change of current multiplied by the inductance. This means that as the current increases or decreases, the voltage across the inductor will also change.

## 4. How does the voltage across a capacitor change over time?

When a capacitor is connected to a voltage source, it will initially have no voltage across it. As the capacitor charges, the voltage across it will increase until it reaches the same voltage as the source. If the source is removed, the voltage across the capacitor will decrease over time as it discharges.

## 5. What is the time constant of an RC or RL circuit?

The time constant of an RC or RL circuit is a measure of how quickly the circuit will reach a steady state after a change in current or voltage. It is equal to the product of the resistance and capacitance (for an RC circuit) or the resistance and inductance (for an RL circuit). A larger time constant means the circuit will take longer to reach a steady state.

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