Question

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

• A. $3A$
• B. $4A$
• C. $7A$
• D. $5A$

Answer 1

The correct option is D $5A$

Quantity of the heat liberated in the ammeter o resistance $R$

$\left(i\right)$ Due to direct current of $3A=\frac{3^{2}R}{J}$

$\left(ii\right)$ Due to alternate current of $4A=\frac{4^{2}R}{J}$

Total heat produced per second

$=3A=\frac{3^{2}R}{J}+4A=\frac{4^{2}R}{J}=\frac{25R}{J}$

Let the equivalent alternating current be $I$ virtual ampere.

$\therefore \frac{I^{2}R}{J}=\frac{25R}{J}$

or $I=5A$