#

# LR Circuits

"A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective"
Edward Teller

- As we have seen, due to Faraday's Law, an induced emf will appear in any loop/coil/circuit in which the current (and therefore the magnetic field) changes with time. Certain circuit elements have a larger (self) inductance than others - the solenoid is the most obvious example of a circuit element with a large inductance.

- An ideal inductance (L) has no resistance and is represented by the following symbol .

- Placing an inductance (L) and a resistance (R) in a simple circuit gives us the "LR" circuit, at right. When the switch is closed to include the power supply in the circuit we can apply Kirchoff's loop theorem to obtain the following equation,

> Note that in applying the loop theorem we make use of the fact that the induced emf across the inductance opposes the changing emf that causes it.

- The solution of this differential equation is given by,

> shown at right, where Imax is ε/R . Also shown is the time dependence of the voltage across the inductance.

- The time constant of the inductance, given by is a measure of the time needed for the current in the circuit to reach 63% of its maximum value.

- Taking the power supply out of the circuit leads to an even simpler differential equation

> the solution of which is
> shown at right. In this figure I0 = ε/R.

This girl said she recognized me from the vegetarian club, but I'd never met herbivore.

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu