Question

For the circuit shown in Figure the rms current is

• A. $I_0$
• B. $I_0/\sqrt{2}$
• C. $I_0/\sqrt{3}$
• D. $I_0/2$

Answer 1

The correct option is C $I_0/\sqrt{3}$

$I=\frac{2I_{0}t}{T}when0<t<T/2$

$I=2I_0(t-T)/TwhenT/2<t<T$
$I_{rms}^2=\frac{I}{T}[{\int }_0^{T/2}{I}^{2}dt+{\int }_{T/2}^T{I}^{2}dt]$
$\frac{I}{T}{\int }_0^{T/2}{\left(\frac{2I_{0}t}{T}\right)}^{2}dt$
$+\frac{1}{T}{\int }_{T/2}^T{\left(\frac{2I_{0}D}{T}\right(t-T\left)\right)}^{2}dt$
$I_{rms}=I_0/\sqrt{3}$