Question

An A.C. voltage v=80sin120πt volts is applied across a 24.0 – Ω resistor. What will an ammeter connected in series with the resistor read?

Answer 1

Given:

The voltage applied,

`V=80\sin(120\pi t)`

The resistance of the resistor, R=24.0 Ω

To find:

The reading in the ammeter.

Step-by-step explanation:

An ac ammeter connected in series with the resistor reads the root mean square value of the current, i.e., I_rms.

Comparing the given equation of the voltage to the standard equation,

`V=V_0\sin(\omega t)`

We get, V₀=80 V

The root mean square value of the voltage is given by the equation,

`V_(rms)=(V_o)/(√(2))`

On substituting the known values,

`\begin{gathered} V_(rms)=(80)/(√(2)) \\ =56.6\text{ V} \end{gathered}`

Thus the value of I_rms is calculated by the equation,

`I_(rms)=(V_(rms))/(R)`

On substituting the known values,

`\begin{gathered} I_(rms)=(56.7)/(24.0) \\ =2.4\text{ A} \end{gathered}`

Final answer:

Thus the reading of the ac ammeter connected in series with the resistor is 2.4 A.