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 8A. What will be reading of each ammeter if dc and ac current flow simulataneously through the circuit?

Options

A. dc=6 A, ac=10A
B. dc=3 A, ac=5A
C. dc=5 A, ac=8A
D. dc=2 A, ac=3A

Answer

A

Explanation

Resultant current is superposition of tow currents, i.e.
I(instantaneous total current ) `=6+(I_0) sin omega t`
dc ammeter will read average value
`=bar(6+(I_0)sin omega t) = 6` `(: Bar((I_0) sin omega t =0))`
ac ammeter will read
`=sqrt((bar(6+(I_0)sin omega t^(2)))`
`=sqrt(bar(36+12 I_(0) sin omega t +I_(0)^(2) sin ^(2)omega t))` (`because bar(I_(0)si omega t =0))`
since `bar(sin^(2) ometa t)=1/2 and (I_(rms))=8=(I_0)/(sqrt(2) implies (I_0)= 8 sqrt(2)A`
Therefore ac reading
`=sqrt(36 + (I_(0)^(2))/(2)) = sqrt(36 + 64) = 10 A`.