What is Ohm’s Law?

Ohm’s Law states that the voltage v(t)across a resistor R is directly proportional to the current  i(t)flowing through it. 

v(t) ∝ i(t)

v(t) =R .i(t)

This general statement of Ohm’s Law can be extended to cover inductance's and capacitors as well under alternating current conditions and transient conditions. This is then known as the Generalized Ohm’s Law. This may be stated as 

v(t) = Z(p) . i(t),  where p = d/dt = differential operator 

Z(p)is known as the impedance function of the circuit, and the above equation is the 

differential equation governing the behavior of the circuit.

For a resistor,  Z(p) = R 

For an inductor Z(p) = Lp 

For a capacitor,  Z(p) = 1/pC

In the particular case of alternating current,  p = jω so that the equation governing circuit 

behavior may be written as 

V = Z(jω). I 

For a resistor,  Z(jω) = R 

For an inductor Z(jω) = jωL

For a capacitor,  Z(jω) = 1/C jω