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, the ac ammeter shows $$8$$ A. What will be reading of each ammeter if dc and ac currents flow simultaneously through the circuit?

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, the ac ammeter shows $$8$$ A. What will be reading of each  ammeter if dc and ac currents flow simultaneously through the circuit?

Infinity Learn · Accepted Answer

Resultant current is superposition of two currents, i.e., I (instantaneous$$ total $$current) $$=$$ $$6+I0$$ $$sin$$ ωt dc ammeter will read average $$value=6+I0sin$$ω$$t=6$$                   $$($$∴$$I0sin$$ω$$t=0)ac$$ ammeter will $$read=6+I0sin$$ω$$t2=36+12I0sin$$ω$$t+I02sin2$$ωt¯               ∴$$I0sin$$ω$$t=0Since$$ $$sin2$$ ω$$t=12$$ and $$Irms=8=I02$$⇒$$I0=82ATherefore$$, ac $$reading=36+I022=36+64=10A$$

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