Q. An AC ammeter is used to measure current in a circuit. When a given direct current passes through the circuit, the AC ammeter reads 3 A. When another alternating current passes through the circuit, the AC ammeter reads 4 A. Then the reading of this ammeter, if DC and AC flow through the circuit simultaneously, is

Solution:

Quantity of heat liberated in the ammeter ofresistancc
(i) due to direct current of 3 A
$ = [ (3)^2 \, R \, / \, J ) ] $
(ii) due to alternating current of 4 A
$ = [ (4)^2 \, R \, / \, J ) ] $
$ \therefore$ Total heat produced per second
= $ \frac{ ( 3)^2 \, R }{ J } + \frac{ ( 4)^2 \, R }{ J } = \frac{ ( 25 \, R }{ J } $
Let the equivalent alternating current be 1 virtual ampere; then
$ \frac{ i^2 \, R }{ J} = \frac{ ( 25 \, R }{ J } $
I = 5 A

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