Ph272- General Physics II (Electricity and Magnetsism)

Lecture 18: Ch. 30 - Inductance and LR Circuits

Key Topics

Overview

• A voltage (or EMF) develops across a conducting loop (or coil) when a time-varying current passess throught it. (Analog: A voltage develops across a capacitor when charges are deposited on the capcitor plates). The EMF depends on the self-inductance (or inductance for short) of the loop. (Analog: The voltage across a capacitor depends on the capacitance). Inductance is like an inertia, it opposes changes in current. Capacitance opposes changes in voltage
• L-R circuit: Current cannot change instantaneous when there is inductance. There is a time constant (L/R) which determines how long it takes the current to cchange its value.
• "Charging an inductor":Change the current from zero to non-zero takes energy (or work). This energy is stored in the inductor. We can express the stored energy in terms of inductance and current or in terms of the magnetic field.

Inductance

• Mutual Inductance: If you have two conducting loop close by. Applying a time-varing current in one loop will induce an EMF in the other loop. The induced EMF (in loop 2) is proportional to the time-derivative of current (in loop 1), the proportionality constant is called the mutual inductance.
• Self-inductance: There is also an EMF induced on loop 1 (self-inductance). This is called "back" EMF because this EMF will produce a current opposes to the changes.
•  

-> Do Problem 23-9, 23-11, P. 774.

LR-circuit

• Circuit setup: We have an inductor in series with a battery source and a resistor.
• What are the initial conditions?

What is the initial current?

What is the initial voltage across the resistor?

What is the voltage across the inductor

• Physical Process: As time goes by, what happens?

The current will rise slowly but continously from zero (At steady state, what is the "maximum" current?)

How is the voltage across the resistor change with time?

How is the voltage across the inductor change with time?

Can you guess the mathematical functions for these curves?

• Set up differential equation for I(t) : (Do this in class) - This is a "first-order, linear, inhomogenous" differential equation. In physics, inhomogenous DE means there is a driving term (the battery)
• Solve the differential equation and match the initial condition. The solution of an inhomogenous DE consists of a steady state part and a transcient part.

Energy stored

• Energy stored: Eq. 26-33. (in terms of inductance and current)
• Energy stored: Eq. 26-24 (in terms of magnetic field)

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