The peak current through an inductor is 10 mA. What is the peak current if the emf peak voltage is doubled (at the original frequency)?

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Understand the relationship between the peak current and the peak voltage in an inductor. The peak current \( I_{peak} \) in an inductor is related to the peak voltage \( V_{peak} \) by the formula: \( I_{peak} = \frac{V_{peak}}{\omega L} \), where \( \omega \) is the angular frequency and \( L \) is the inductance.

Note that the angular frequency \( \omega \) is given by \( \omega = 2 \pi f \), where \( f \) is the frequency. Since the problem states that the frequency remains unchanged, \( \omega \) and \( L \) are constants in this scenario.

When the peak voltage \( V_{peak} \) is doubled, substitute \( 2V_{peak} \) into the formula for \( I_{peak} \): \( I_{peak} = \frac{2V_{peak}}{\omega L} \).

Compare the new peak current to the original peak current. The original peak current is \( I_{original} = \frac{V_{peak}}{\omega L} \). The new peak current is twice the original peak current because \( \frac{2V_{peak}}{\omega L} = 2 \cdot \frac{V_{peak}}{\omega L} \).

Conclude that doubling the peak voltage results in doubling the peak current. Therefore, the new peak current is \( 2 \cdot 10 \text{ mA} \).

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주요 개념

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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. The inductance value, measured in henries (H), determines how much voltage is induced across the inductor when the current changes. This relationship is crucial for understanding how inductors respond to changes in current and voltage.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This fundamental principle, expressed as V = IR, is essential for analyzing circuits, including those with inductors, as it helps determine how changes in voltage affect current.

Peak Voltage and Current Relationship

In AC circuits, the peak voltage and peak current are related through the impedance of the circuit, which includes resistance and reactance. When the peak voltage is increased while keeping the frequency constant, the peak current will also increase, assuming the impedance remains unchanged. This relationship is vital for predicting how changes in voltage affect current in inductive circuits.