Respuesta :
Given:
The voltage applied,
[tex]V=80\sin(120\pi t)[/tex]The resistance of the resistor, R=24.0 Ω
To find:
The reading in the ammeter.
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,
[tex]V=V_0\sin(\omega t)[/tex]We get, V₀=80 V
The root mean square value of the voltage is given by the equation,
[tex]V_{rms}=\frac{V_o}{\sqrt{2}}[/tex]On substituting the known values,
[tex]\begin{gathered} V_{rms}=\frac{80}{\sqrt{2}} \\ =56.6\text{ V} \end{gathered}[/tex]Thus the value of I_rms is calculated by the equation,
[tex]I_{rms}=\frac{V_{rms}}{R}[/tex]On substituting the known values,
[tex]\begin{gathered} I_{rms}=\frac{56.7}{24.0} \\ =2.4\text{ A} \end{gathered}[/tex]Final answer:
Thus the reading of the ac ammeter connected in series with the resistor is 2.4 A.
