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### Alternating Current

# Phase relation between voltage and current

Even though both the voltage v and current i are both
functions of time, they are **in phase** with each other so
their ratio is a constant. Being **in phase** means they both
reach their maxima at the same time, both pass through zero at the
same time, and both reach their minima at the same time.

As the voltage v increases, the current i increases proportionally
so that the ratio of v/i remains a constant. This constant is the
resistance R. While we can write this resistance as

it might be mistaken to imply that the resistance varies with
time; the resistance R is a constant. We can also write the
resistance R as

where the voltage or potential difference is given by

v = v(t) = V_{max} sin t
= V_{o} sin t
and the current is given by

i = i(t) = I_{max} sin t
= I_{o} sin t
V_{max} , V_{o} , I_{max} , and
I_{o} are just ordinary numbers or constants so they are
written as capitals.

(c) Doug Davis, 2002; all rights reserved