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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?

dc = 6 A, ac = 10 A
dc = 3 A, ac = 5 A
dc = 5 A, ac = 8 A
dc = 2 A, ac = 3 A

detailed solution

Correct option is A

Resultant current is superposition of two currents, i.e., I (instantaneous total current) = 6+I0 sin ωt dc ammeter will read average value=6+I0sinωt=6                   (∴I0sinωt=0)ac ammeter will read=6+I0sinωt2=36+12I0sinωt+I02sin2ωt¯               ∴I0sinωt=0Since sin2 ωt=12 and Irms=8=I02⇒I0=82ATherefore, ac reading=36+I022=36+64=10A

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A direct current of 5 A is superimposed on an alternating current .I=10 sin ωtflowing through a wire. The effective value of the resulting current will be

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