## UY1: Resistors, Inductors & Capacitors In A.C. Circuits

Resistor In An A.C. Circuit Consider a resistor with resistance R through which there is a sinusoidal current: $$i = I \cos{\omega t}$$ From Ohm’s Law, \begin{aligned} v_{R} &= iR \\ &= \left( IR \right) \cos{\omega t} \\ &= V_{R} \cos{\omega t} \end{aligned} The current $i$ is in phase with the voltage $v_{R}$ The instantaneous power $p$ delivered to a …

## UY1: Phasors & Alternating Currents

Any device that supplies a sinusoidally varying voltage (potential difference) $$v = V \cos{\omega t}$$ , where V is the voltage amplitude, or current $$i = I \cos{\omega t}$$ , where I is the current amplitude, is an alternating current (ac) source with angular frequency: \begin{aligned} \omega &= 2 \pi f \\ &= \frac{2 \pi}{T} \end{aligned} You can represent the …

## UY1: R-L Circuit

A circuit that includes both a resistor and an inductor, and possibly a source of e.m.f., is called an R-L circuit. Suppose both switches are open to begin with, and then at some initial time $t = 0$, we close switch $S_{1}$. Let $i$ be the current at some time $t$ after $S_{1}$ is closed and let $\frac{di}{dt}$ be its …

## UY1: Self-Inductance & Inductors

Consider a coil of wire with current $i$ flowing through it that is changing at $\frac{di}{dt}$. The current $i$ in the circuit causes a magnetic field $\vec{B}$ in the coil with N turns of wire, and hence an average magnetic flux $\Phi_{B}$ through each turn of the coil. From Faraday’s Law, the induced e.m.f. is given by: $$\epsilon =-N \frac{d\Phi_{B}}{dt}$$ …