# Voltage across inductor in AC

http://physics.bu.edu/~duffy/PY106/ACcircuits.html

The voltage across inductor is V=IXL but from the graph this doesn't seem to be true so what does it show ? Same for Capacitors

• Why do you think that these graphs are false? – G36 Mar 1 '18 at 14:50
• @G36 when voltage is maximum then current is zero which kinda violates this formulae in my opinion – Scáthach Mar 1 '18 at 15:38
• In a steady state for a sinusoidal extortion, the current in the inductor is lagging the voltage by 90 degrees. So if we ignore the phase shift we can find the "magnitude" of a current using this equation IL = VL/XL. And remember that the current is lagging the voltage by 90 degrees. electronics.stackexchange.com/questions/288380/… – G36 Mar 1 '18 at 15:55
• @G36 so we can't use this formulae for instantaneous values of current and voltage,right?Only for RMS values values – Scáthach Mar 1 '18 at 21:22
• No, you can use this equation for instantaneous values also. v(t) = Vpeak/XL * sin (ωt) and for current i(t) = Vpeak/XL * sin (ωt - 90 degrees) – G36 Mar 2 '18 at 15:08

The voltage across an inductor is V = $L\dfrac{di}{dt}$ so if the steady state voltage is a sinewave then the current, when differentiated is a sine wave. This means the current is an inverted cosine wave as shown in the picture.

The voltage across inductor is V=IXL

If you are reffering to RMS voltage and current then that is correct but, of course RMS voltages and currents do not embody the notion of phase angle (as seen in the diagram above). So the ratio of the voltage and current magnitudes equals the magnitude of the impedance but, behind this simplistic notion lies a deeper truth.

• So this formulae applies only for rms values......but what about instantaneous current and voltage – Scáthach Mar 1 '18 at 15:40
• The formula I gave in my answer is for an inductor's instantaneous values i.e. if current is rising at 1 amp per second and the inductance is 1 henry, the voltage will be 1 volt for example. – Andy aka Mar 1 '18 at 15:45
• $V = L\dfrac{di}{dt}$ allows you to calculate instantaneous values. It's the base formula for the relationship between V and I in an inductor and from this is derived (via simplification) the RMS formula you have used. – Andy aka Mar 1 '18 at 15:51