Question

Show that the current and voltage are in phase in an ac circuit containing resistance only.

Answer 1

The Phase difference is
tan(α) = (Xl -Xc) /R
Now, if only Resistance is present then, Xl=Xc=0
therefore,
tan(α) = 0 or α=0
which means that the current and voltage are in phase..

Answer 2

Answer:

In a circuit containing resistance only, voltage and current are in phase.

Explanation:

In contrast to direct current (DC), which only flows in one direction, alternating current (AC) is an electric current that periodically reverses direction and constantly changes its magnitude over time.

Because there is less time to change the voltage when the frequency of the voltage is greater, the current must be bigger. Consequently, as the capacitance and frequency rise, the current rises.

The electrical current that flows through an AC resistance varies with time and is represented by the expression, $I(t)=I \sin (\omega t+\theta)$

Now by ohm's law, $V=I R$

So, for the AC circuit, $V=I R \sin (\omega t+\theta)$

$c=c_0 \sin u t \ldots . & .....(i)$

Potential drop  $e & =i R \ldots \ldots$$(ii)$

$i R & =c_0 \sin \omega t$

$i & =\frac{e_0}{R} \sin w t \ldots(iii)$

Peak value io $=\frac{e_0}{R}$

current = $i$= $i_0 \text { Sin wit }$.....$(iv)$

For pure resistive circuit, phase difference=0

In a circuit containing resistance only, both $\mathrm{V}$ and I have zero phase difference and hence are in phase.

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