It has been proposed to use large inductors as energy storage devices. (b) If the amount of energy calculated in part (a) is stored in an inductor in which the current is 80.0 A, what is the inductance?

Verified step by step guidance

1. Identify the formula for the energy stored in an inductor, which is given by $E = \frac{1}{2} L I^2$, where $E$ is the energy, $L$ is the inductance, and $I$ is the current flowing through the inductor.
2. Rearrange the formula to solve for the inductance $L$. This can be done by isolating $L$ on one side of the equation: $L = \frac{2E}{I^2}$.
3. Substitute the value of the current $I = 80.0 \, \text{A}$ into the rearranged formula.
4. Use the value of the energy $E$ calculated in part (a) and substitute it into the formula.
5. Calculate the value of $L$ using the substituted values to find the inductance required to store the specified amount of energy.

Key Concepts

Inductance

Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. It is measured in henries (H) and is defined as the ratio of the induced electromotive force (emf) to the rate of change of current. Higher inductance means more energy can be stored for a given current.

Energy Stored in an Inductor

The energy (E) stored in an inductor can be calculated using the formula E = (1/2) L I², where L is the inductance in henries and I is the current in amperes. This relationship shows that the energy stored increases with the square of the current, highlighting the importance of both inductance and current in energy storage applications.

Current

Current is the flow of electric charge in a circuit, measured in amperes (A). In the context of inductors, the current flowing through the inductor directly affects the amount of energy stored in its magnetic field. Understanding the relationship between current and inductance is crucial for calculating the energy storage capacity of inductors.