A circuit consisting of a capacitor and a coil in series is connected to the mains. Varying the capacitance of the capacitor, the heat power genergated in the coil was increased `n=1.7` times. How much `(` in per cent `)` was the value of ` cos varphi` changed in the process ?

Explanation

`P=(V^(2)R)/(R^(2)+(X_(L)-X_(C))^(2))`
Varying the capacitor does not change `R` as if `P` increases `n` times
`cancel(Z)=sqrt(R^(2)+(X_(L)-X_(C))^(2))` must decreases ` sqrt(n)` times
Thus `cos varphi=(R)/( cancel(Z))` increases `sqrt(n)` times
`:. % `increase in `cos varphi=(sqrt(n)-1)xx100%=30.4 %.`