What is the peak current supplied by the emf in FIGURE P32.42?

Verified step by step guidance

1. Identify the components of the circuit in FIGURE P32.42. Typically, such problems involve an AC circuit with a resistor, inductor, and/or capacitor. Note the values of resistance (R), inductance (L), capacitance (C), and the peak voltage of the emf (V₀).
2. Understand that the peak current (I₀) in an AC circuit is determined by the relationship: $I$₀=V₀Z, where $Z$ is the impedance of the circuit.
3. Calculate the impedance $Z$ of the circuit. For a series RLC circuit, the impedance is given by: $Z=\sqrt{R^2+{(}^X}$_L-X_C)2, where $X$_L=ωL is the inductive reactance and $X$_C=1ωC is the capacitive reactance. Here, $\omega =2\pi f$ is the angular frequency of the AC source.
4. Substitute the given values of resistance, inductance, capacitance, and frequency into the formulas for $X$_L, $X$_C, and $Z$. Simplify the expressions to find the total impedance of the circuit.
5. Finally, use the formula $I$₀=V₀Z to calculate the peak current. Substitute the peak voltage of the emf and the calculated impedance into the equation to determine the peak current.

Key Concepts

Electromotive Force (emf)

Electromotive force (emf) is the voltage generated by a source, such as a battery or generator, when no current is flowing. It represents the energy per unit charge provided by the source to move charges through a circuit. Understanding emf is crucial for analyzing how much current can be supplied under different circuit conditions.

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 relationship is expressed as I = V/R. It is fundamental for calculating the peak current in a circuit when the emf and resistance are known.

Peak Current

Peak current refers to the maximum instantaneous current that can flow in a circuit when the voltage is at its highest point. In the context of an emf source, it is determined by the source's voltage and the total resistance in the circuit. Understanding peak current is essential for assessing the performance and safety of electrical systems.