It takes `t_(0)` hours for a direct current `I_(0)` to charge a storage battery. How long will it take to charge such a battery from the mains using a half`-` wave rectifier, if the effective current value is also equal to `I_(0)` ?

Explanation

The `a.c.` current must be
`I=I_(0) sqrt(2) sin omegat `
Then `D.C.` component of the rectified current is
`lt I^(' ) gt =(1)/(T) int _(0)^(T//2)I_(0)sqrt(2) sin omegat dt`
`=I_(0) sqrt(2)(1)/(2pi)int _(0)^(pi)sin theta d theta`
`=(I_(0)sqrt(2))/( pi)`
Since the charge deposited must be the same
`I_(0)t_(0)=(I_(0)sqrt(2))/(pi)t` or `t=(pit_(0))/( sqrt(2))`
The answer is incorrect .