A dc ammeter and a hot wire ammeter are connected to a circuit in a 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?

Resultant current is superposition of two currents, i.e. I(instantaneous total current ) = $6+I_0\sin \omega t$

Dc ammeter will read average value

$\overline{6+I_0\sin \omega t}=6\left(\because \overline{I_0\sin \omega t=0}\right)$

Ac ammeter will read

$\sqrt{{\left(\overline{6+I_0{\sin }^2\omega t}\right)}^2}$

$\sqrt{36+12I_0\sin \omega t+I_0{}^2{\sin }^2\omega t}$

$\left(\because \overline{I_0\sin \omega t=0}\right)$

Since $\overline{{\sin }^2\omega t}=\frac{1}{2}$ and $I_{rms}=8=\frac{I_0}{\sqrt{2}}$

Ac reading

$=\sqrt{36+\frac{I_0{}^2}{2}}=\sqrt{36+64}=10A$