What is the potential difference across a 10.0 mh inductor if the current through the inductor drops from 120 ma to 60.0 ma in 16.0 μs ?
The Correct Answer and Explanation is:
To calculate the potential difference (voltage) across a 10.0 mH inductor when the current changes, we can use the formula derived from Faraday’s law of electromagnetic induction:
[
V = L \frac{\Delta I}{\Delta t}
]
Where:
- ( V ) is the potential difference (voltage) across the inductor,
- ( L ) is the inductance (in henries),
- ( \Delta I ) is the change in current (in amperes),
- ( \Delta t ) is the change in time (in seconds).
Given Values:
- Inductance, ( L = 10.0 \, \text{mH} = 10.0 \times 10^{-3} \, \text{H} )
- Initial current, ( I_i = 120 \, \text{mA} = 120 \times 10^{-3} \, \text{A} = 0.120 \, \text{A} )
- Final current, ( I_f = 60.0 \, \text{mA} = 60.0 \times 10^{-3} \, \text{A} = 0.060 \, \text{A} )
- Time interval, ( \Delta t = 16.0 \, \mu\text{s} = 16.0 \times 10^{-6} \, \text{s} )
Calculating the Change in Current:
[
\Delta I = I_f – I_i = 0.060 \, \text{A} – 0.120 \, \text{A} = -0.060 \, \text{A}
]
Substituting Values:
Now we can substitute the values into the formula:
[
V = L \frac{\Delta I}{\Delta t} = 10.0 \times 10^{-3} \, \text{H} \cdot \frac{-0.060 \, \text{A}}{16.0 \times 10^{-6} \, \text{s}}
]
Calculating the right side:
[
V = 10.0 \times 10^{-3} \cdot \frac{-0.060}{16.0 \times 10^{-6}} \approx 10.0 \times 10^{-3} \cdot -3750 \approx -37.5 \, \text{V}
]
Conclusion:
The potential difference across the inductor is approximately −37.5 V. The negative sign indicates that the voltage is in the opposite direction of the current flow, which is characteristic of inductors when the current decreases.
Explanation:
Inductors resist changes in current, and when the current decreases, the inductor generates a voltage in the direction that opposes this decrease (Lenz’s Law). This potential difference is essential in various applications, such as in filters, transformers, and energy storage systems, where controlling the flow of current is crucial. Understanding this principle is fundamental in electrical engineering and circuit design, as it governs how inductors behave in alternating current (AC) circuits and during transient conditions.