Question

Find the effective value or rms value of an alternating current that changes according to the law (All quantities are in S.I. unit and symbols have their usual meaning)

I=10, when $0<t<T/8;I=0$, when $\frac{T}{8}<t<\frac{T}{2}$

I=-10, when $\frac{T}{2}<t<\frac{5}{8}T$; I = 0, when $\frac{5}{8}T,t<T$; I = 10, when $T<t<\frac{9}{8}T$

Answer 1

We solve this problem using the fact that the effective value of an alternating current is the value of a direct current that produces the same quantity of heat in a conductor the alternating current during the same time The heat produced by the AC current during on time period from 0 to T is

$H={10}^{2}R\frac{T}{8}+0+{10}^{2}R\frac{T}{8}+0$

$H={10}^{2}R\frac{T}{4}...\left(1\right)$

In the same time interval 0 to T heat produced by constant direct current I, would have been

$H^{\prime }=I^{2}RT...\left(2\right)$

$H=H^{\prime }\Rightarrow I^{2}RT={10}^{2}R\frac{T}{4}$

$\Rightarrow I=\frac{10}{2}$

effective value or rms value of required current is 5