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 $6A$. When AC current flows through circuit, the AC ammeter shows $8A$. What will be reading of each ammeter, if $DC$ and $AC$ currents flow simultaneously through the circuit?

• A. DC =6 A , AC =10 A
• B. DC =3 A , AC =5 A
• C. DC =5 A , AC =8 A
• D. DC =2 A , AC =3 A

Answer 1

Answer: (A)

Resultant current is super-position of two currents
i.e., $I$ (instantaneous total current) $=6+I_0\sin \omega t$
DC ammeter will read average value
$=\overline{6+I_0\sin \omega t}=6\left(\therefore \overline{I_0\sin \omega t}=0\right)$
AC ammeter reading
$=\sqrt{\overline{{\left(6+I_0\sin \omega t\right)}^2}}$
$=\sqrt{36+12I_0\sin \omega t+I_0^2{\sin }^2\omega t}$
$\left(\therefore \overline{I_0\sin \omega t}=0\right)$
Since $\overline{{\sin }^2\omega t}=\frac{1}{2}$ and $I_{\text{r.m.s. }}=8=\frac{I_0}{\sqrt{2}}$
$\therefore$ AC ammeter reading
$=\sqrt{36+\frac{I_0^2}{2}}=\sqrt{36+64}=10A$