Question

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

• A. 3 A
• B. 4 A
• C. 7 A
• D. 5 A

Answer 1

Answer: (D)

Quantity of heat liberated in the ammeter of resistance
(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
= $\frac{(3{)}^{2}R}{J}+\frac{(4{)}^{2}R}{J}=\frac{25R}{J}$
Let the equivalent alternating current be I virtual ampere; then
$\frac{I^{2}R}{J}=\frac{25R}{J}$
I = 5 A