An AC voltage source is applied across an R-C circuit. Angular frequency of the source is `omega`, resistance is R and capacitance is C. The current registered is I. If now the frequency of source is changed to `omega/2` (but maintaining the same voltage), the current in the circuit is found to be two third. calculate the ratio of reactance to resistance at the original frequency `omega` .

Explanation

According to the given problems.
`I=(V)/(Z)=(V)/([R^(2)+(1//Comega)^(2)]^(1//2))......(i)`
`and (I)/(2)=(V)/([R^(2)+(3//Comega)^(2)]^(1//2))......(2)`
Substituting the value of I from Equation (i) and (2).
`4(R^(2)+(1)/(2C^(2)omega^(2)))=R^(2)+(9)/(C^(2)omega^(2)), i.e. (1)/(C^(2)omega^(2))=(3)/(5)R^(2)`
`"So that ", (X)/(R)=((1//Comega))/(R)=((3)/(5)R^(2))^(1//2)/(R)=sqrt((3)/(5))`