Question 43: AC fundamentals

Question

A DC ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through circuit, the DC ammeter shows 6 A. When AC current flows through circuit, what is the average readings in DC ammeter and the AC ammeter, if DC and AC currents flows simultaneously through the circuit?

Accepted Answer

Resultant current is superposition of two currents, i.e. $$I$$ (instantaneous total current)
$$=6+I_0 \sin \omega t$$
$$\mathrm{DC}$$ ammeter will read average value
$$\begin{aligned}
& =\overline{6+I_0 \sin \omega t}\
& =6 \mathrm{~A}
\end{aligned}$$
$$\left(\because \overline{I_0 \sin \omega t}=0ight)$$
$$\mathrm{AC}$$ ammeter will read average value
$$\begin{aligned}
& =\sqrt{\overline{\left(6+I_0 \sin ^2 \omega tight)^2}} \
& =\sqrt{36+12 I_0 \sin \omega t+I_0^2 \sin ^2 \omega t}\end{aligned}$$
$$\left(\because \overline{I_0 \sin \omega t}=0ight)$$
Since, $$\overline{\sin ^2 \omega t}=\frac{1}{2}$$ and $$I_{\mathrm{rms}}=8=\frac{I_0}{\sqrt{2}}$$
$$\begin{aligned}
	herefore \mathrm{AC} 	ext { reading }=\sqrt{36+\frac{I_0^2}{2}} & =\sqrt{36+64} \
& =10 \mathrm{~A}\end{aligned}$$

Answer

DC = 6 A, AC = 10 A

Answer

DC = 3 A, AC = 5 A

Answer

DC = 5 A, AC = 8 A

Answer

DC = 2 A, AC = 3 A

AC fundamentals

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