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

Answer

A

Explanation

Resultant current is supper-position of two currents i.e, `I`(instantaneous total current) `=6+I_(0) sin omegat`
`DC` ammeter will read average value
`=bar(6+I_(0)sin omegat)=6 (`:.` bar(I_(0) sin omegat=0))`
`AC` ammeter will read
`sqrt(bar((6+I_(0)sin^(2) omegat)^(2)))`
`=sqrt(36+12I_(0)sin omegat+I_(0)^(2)sin^(2) omegat)`
`(`:.` bar(I_(0)sin omegat=0))`
Since `bar(sin^(2) omegat)=1/2` and `I_(r.m.s)8 (I_(0))/(sqrt(2))`
`:. AC` reading
`=sqrt(36+(I_(0)^(2))/2) =sqrt(36+64)=10 A`