Help with a circuit (inductors)

In summary, the problem asks to find the current (i(t)) for t ≥ 0 in a circuit with a 2.5mH inductor and a voltage of 10 cos(1000t)mV. It also asks to find the power and energy in the circuit. The power is the rate at which energy changes and is calculated using V * i, where V is the voltage and i is the current. In an AC circuit, V and i are varying with time and can be out of phase depending on the reactance. To find i(t), one can use the equation V(t) = L * di/dt and solve for i(t) using the given voltage.
  • #1
TSizzle55
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0

Homework Statement


The voltage across an L = 2.5mH inductor is v(t) = 10 cos(1000t)mV, with i(0) = 1 mA.
(a) Find i(t) for t ≥ 0.
(b) Find the power and energy.

Homework Equations


V= L * di/dt
Power= V * i
V * i= L * i * (di/dt)

The Attempt at a Solution


I really don't know where to start. I'm just looking for an explanation of what the problem is asking (What does 'Find the power and energy' mean?). That would be really helpful, thanks.
 
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  • #2
The power is the rate at which energy changes or the rate at which it is supplied or stored.

In DC, power is pretty straightforward. P = VI, and V and I are constant.

In AC, V and I are varying with time and out of phase depending on the reactance in the circuit/component.

Presumably one's textbook describes voltage, current and power with respect to an inductor and AC.

Given V(t) = L * di/dt, how would one find i(t) if one knows v(t)?
 
  • #3


Hi there! It looks like you are being asked to solve for the current (i) in the circuit, as well as the power and energy associated with the inductor.

To find i(t), you can use the equation V = L * di/dt, where V is the voltage across the inductor (given as 10 cos(1000t)mV) and L is the inductance (given as 2.5mH). You can solve for di/dt and then integrate to find the current i(t).

To find the power, you can use the equation P = V * i, where P is power, V is voltage, and i is current. You can substitute in the values you found for V and i to solve for power.

To find the energy, you can use the equation E = 1/2 * L * i^2, where E is energy, L is inductance, and i is current. You can substitute in the value you found for i to solve for energy.

I hope this helps! Let me know if you have any further questions.
 

1. What is an inductor and how does it function in a circuit?

An inductor is an electrical component that stores energy in the form of a magnetic field. It consists of a coil of wire and its main function is to resist changes in current flow. When current flows through an inductor, it causes a magnetic field to form around the coil. This magnetic field stores energy, and when the current is removed, the magnetic field collapses and releases the stored energy back into the circuit. This property of inductors makes them useful for controlling the flow of current in a circuit.

2. How do I calculate the inductance of an inductor?

The inductance of an inductor can be calculated using the formula L = NΦ/I, where L is the inductance in henries, N is the number of turns in the coil, Φ is the magnetic flux, and I is the current flowing through the inductor. This formula can be rearranged to calculate any of the variables, given the values of the others.

3. What is the difference between inductors and capacitors?

Inductors and capacitors are both components used in electronic circuits, but they have different functions. While inductors store energy in the form of a magnetic field, capacitors store energy in the form of an electric field. Additionally, the behavior of inductors and capacitors in a circuit is opposite to each other. An inductor resists changes in current, while a capacitor resists changes in voltage.

4. How do I choose the right inductor for my circuit?

The right inductor for a circuit depends on several factors, such as the desired inductance, current rating, and frequency of the circuit. To choose the right inductor, you should first determine the required inductance and current rating for your circuit. Then, you can select an inductor with a suitable inductance value and current rating. Additionally, the frequency of the circuit should also be considered, as inductors have different characteristics at different frequencies.

5. Can inductors be connected in series or parallel?

Yes, inductors can be connected in series or parallel depending on the requirements of the circuit. When connected in series, the total inductance is the sum of the individual inductances. When connected in parallel, the total inductance is calculated using the formula 1/L = 1/L1 + 1/L2 + ... + 1/Ln. Just like other components, the connection of inductors in a circuit should be carefully considered to ensure proper functioning.

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