In the circuit in Fig. P29.47, an emf of 90.0 V is added in...

In the circuit in Fig. P29.47, an emf of 90.0 V is added in series with the capacitor and the resistor, and the capacitor is initially uncharged. The emf is placed between the capacitor and switch $S$, with the positive terminal of the emf adjacent to the capacitor. Otherwise, the two circuits are the same as in Problem 29.47. The switch is closed at $t =$ 0. When the current in the large circuit is 5.00 A, what are the magnitude and direction of the induced current in the small circuit?

Key Concepts

Lenz's Law

Lenz's law determines the direction of the induced current resulting from a changing magnetic flux and states that the induced current will flow in such a direction that its own magnetic field opposes the original change. This law is essential for understanding the directional aspect of the induced current in the secondary circuit relative to the changing magnetic environment created by the primary circuit.

Faraday's Law of Induction

Faraday's law states that the induced emf in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit. This law provides the mathematical framework for calculating the magnitude of the induced emf in a secondary circuit that is linked to a primary circuit with a time-varying current.

Electromagnetic Induction

This is the phenomenon by which a time-varying magnetic field induces an electromotive force (emf) in a nearby circuit. It encompasses the general principles that describe how currents and voltages can be generated by changes in magnetic flux, forming the basis for understanding induced currents in secondary circuits when exposed to a changing magnetic field from a primary circuit.

Mutual Inductance

Mutual inductance quantifies how effectively a change in current in one circuit can induce an emf in a nearby circuit. It plays a crucial role when two circuits are magnetically coupled, as the time-dependent current in one loop creates a varying magnetic flux that penetrates the other loop, leading to an induced emf according to the principles of electromagnetic induction.

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