We need to find:
For the power dissipated to become half of its maximum value, what is the current amplitude?
Step 1: Relation between Power and Current
The average power dissipated in an AC circuit is given by:
P=Irms2RAt resonance, the impedance is purely resistive (
Z=R ), and the current is maximum (
I=Imax ).
So maximum power is:
Pmax=Irms,max2R=()2R=But we only need relative power, so we can use
P∝I2.
Step 2: Condition for half power
We are told
P=Pmax So:
I2R=Imax2RSimplify:
I=So the current amplitude becomes
1∕√2 times its maximum value when the power is half of the maximum.
