Question

A square wave current, switching rapidly between $+0.5A$ and $-0.5A$, is passed through an AC ammeter. The reading shown by ammeter is.

Answer 1

Given:

A square wave current, switching rapidly between $+0.5A$ and $-0.5A$.

Step 1: Formula

We need to find the RMS Power

Formula: $Power\frac{dP}{dt}={I_{rms}}^{2}R$

Step2: Calculation

⇒ $P={\int }_0^T{I_{rms}}^{2}Rdt$

⇒$P={\int }_0^{T/2}{I_{rms}}^{2}Rdt+{\int }_{T/2}^T{I_{rms}}^{2}Rdt$

⇒ $P={\int }_0^{T/2}{(0.5)}^{2}Rdt+{\int }_{T/2}^T{(-0.5)}^{2}Rdt$

⇒ $P=0.25R{\left[T\right]}_0^{T/2}+0.25R{\left[T\right]}_{T/2}^T$

⇒ $P=0.25RT$

⇒ ${I_{rms}}^{2}RT=0.25RT$

⇒ $I_{rms}=0.5Amp$

⇒ The reading shown by the ammeter is $0.5Amp$