Question

One circuit contains only an ac generator and a resistor, and the rms current in this circuit is IR. Another circuit contains only an ac generator and a capacitor, and the rms current in this circuit is IC. The maximum, or peak, voltage of the generator is the same in both circuits and does not change. If the frequency of each generator is tripled, by what factor does the ratio IR/IC change?

Answer 1

1/3 times.

Step-by-step explanation:

Let V₀ be the peak voltage .

IR ( rms ) = ( V₀ / √2 R )

R is value of resistance

IC = ( V₀ ωC / √2 )

( 1 / ωC is reactance of capacitance in ac circuit )

`(I_R)/(I_C) =((V_0)/(√(2)R ) )/((V_0\omega C)/(√(2) ) )`

=
`(I_R)/(I_C) = (1)/(\omega C R)`

When frequency is tripled angular frequency will also be tripled

hence the ratio
`(I_R)/(I_C)` becomes 1/3 times.