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How can CURRENT in a purely capacitive circuit LEAD applied VOLTAGE?

We are all familiar with the fact that in a purely inductive circuit, the current lags behind the applied voltage by a phase difference of /2, while in a purely capacitive circuit, current leads the applied voltage by the same phase difference (/2).

First of all,let us come to the concept of phase.Phase is a mathematical concept .a phase difference of 2? refers to a time difference of one whole time period(t).So,in case of the sinosuidally varying current and voltage in an a.c. circuit,the phase difference can merely be explained as the smallest time difference between the attainment of the peak values of current and voltage.

AS WE KNOW,IN A PURELY INDUCTIVE CIRCUIT,THE CURRENT LAGS BEHIND THE VOLTAGE BY A PHASE DIFFERENCE OF /2,WHICH ERELY INDICATES THAT ON SWITCHINGON THE VOLTAGE,CURRENT DOES NOT INSTANTLY BUILD UP IN THE CIRCUIT.BY THE TIME THE CURRENT REACHES ITS PEAK VAUE,THE VOLTAGE HAS ALREADY

RECEEDED.

LET US IMAGINE THE GRAPHS OF THE VARIATION IN VOLTAGE AND CURRENT.

OUR POINT OF CONCERN IS THE ORIGIN.THE VOLTAGE HAS BEEN APPLIED ACROSS THE ENDS OF THE CIRCUIT,AND SO WITH MAXIMUMVALUE OF VOLTAGE IS AT TIME t = 0,WHERE CURRENT IS ZERO.THAT MEANS THE CURRENT STARTS AT T/4,WHERE T IS THE TIME PERIOD.

THERE IS NO PROBLEM HERE,AS THE IDEA OF THE CURRENT STARTING TO BUILD A LITTLE BIT AFTER THE VOLTAGE IS APPLIED IS ACCEPTABLE.

NOW,LET US CONSIDER A PURELY CAPACITIVE CIRCUIT.AGAIN,AS WE ARE ALL AWARE OF THE FACT THAT IN A CAPACITIVE CIRCUIT,THE CURRENT LEADS THE VOLTAGE BY A PHASE DIFFERENCE OF ?/2,THE GRAPHS REPRESENTING CURRENT AND VOLTAGE ARE REVERSED. SO,ONCE AGAIN,LET US TAKE A LOOK AT WHAT HAPPENS AT TIME t = 0;IT IS CLEAR THAT THE CURRENT HAS RECHED ITS PEAK VALUE,WHILE THERE IS NO VOLTAGE(POTENTIAL DIFFERENCE) ACROSS THE CIRCUIT???.

WAIT A MINUTE!!!! IF THE CURRENT LEADS THE VOLTAGE BY A PHASE OF /2, IT SURELY MEANS THAT THERE IS CURRENT FLOWINGIN THE CIRCUIT EVEN BEFORE THE BATTERY IS SWITCHED ON!!

HOW'S THAT POSSIBLE??CAN THE CAPACITOR READ THE MIND OF THE EXPERIMENTER??

THE SOLUTION TO THIS SEEMINGLY COMPLEX PARADOX IS A SIMPLE INTERPRETATION.

WHEN ONE SAYS THAT THE CURRENT IS LEADING THE POTENTIAL DIFFERENCE BY A PHASE OF /2,IN REALITY IT IS ACTUALLY LAGGING BY A PHASE OF 3/2.WHEN ONE SAYS THAT THE CURRENT LEADS THE VOLTAGE Y T/4,IT ACTUALLY LAGS THE VOLTAGE BY 3T/4.

THIS INTERPRETATION CAN EXPLAIN WHY THERE CANNOT BE ANY CURRENT IN THE CIRCUIT BEFORE THE BATTERY IS SWITCHED ON,WITHOUT VIOLATING ANY MATHEMATICAL FORMULATION.

MATHEMATICAL METHODS AND EXPERIMENTAL PHYSICS ARE MUTUALLY SUPPORTIVE,HOWEVER SOMETIMES WHEN THEY SEEM TO CONTRADICT EACH OTHER,A REINTERPRETATION IS REQUIRED TO AVOID APPARENT DIFFICULTIES IN ITS APPLICATION.

SOURCE:PHYSICS FOR YOU

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