AC Voltage Applied to a Resistor: Definition, Concept, Characteristics, Benefit & Notes

A resistor is an electronic component that opposes the flow of electricity. It is used to control the amount of current and divide the voltage. The unit of resistance is the Ohm (Ω). 

Also Read: NCERT Solutions

When an AC voltage is applied to a resistor (R), the current and voltage remain in phase. This means, when the voltage is at its peak, so is the current. Also, the behaviour of the circuit is governed by Ohm's Law and the properties of AC signal.

Also Read: Class 12 Physics NCERT Solutions

Mathematical Representation 

The applied AC voltage is: $V\left(t\right)=V_0\sin \left(\omega t\right)$

Where,  

• $V_0$ is the peak voltage.

• 𝜔 is the angular frequency (ω=2πf, where 𝑓 is the frequency) 

• t is time 

According to Ohm's Law:

$I\left(t\right)=\frac{V\left(t\right)}{R}=\frac{V_0}{R}\sin \left(\omega t\right)=I_0\sin \left(\omega t\right)$

Where the peak current is expressed as: $I_0=\frac{V_0}{R}$

Phase Relationship: 

V(t) ∝ I(t) 

Power in a Resistor in AC Circuit 

Instantaneous power: $P\left(t\right)=V\left(t\right)\cdot I\left(t\right)=V_0{I}_0{\sin }^2\left(\omega t\right)$

Using ${\sin }^2\left(\omega t\right)=\frac{1-\cos \left(2\omega t\right)}{2}$ we get

$P\left(t\right)=\frac{V_0{I}_0}{2}(1-\cos (2\omega t\left)\right)$

Average power (over a full cycle):

$P_{\mathrm{avg}}=\frac{V_0{I}_0}{2}=V_{\mathrm{rms}}\cdot I_{\mathrm{rms}}$

where, 

$V_{\mathrm{rms}}=\frac{V_0}{\sqrt{2}},I_{\mathrm{rms}}=\frac{I_0}{\sqrt{2}}$

 

Here, we have provided the key characteristics of applying AC voltage to a resistor.

Property	Behaviour in Resistor
Power	Positive
Energy Conversion	Electrical → Heat
Voltage & Current	In Phase
Reactance	None

Important Links:

NCERT Class 11 notes	CBSE Class 11 Physics NCERT notes
Class 11 Chemistry NCERT notes	Maths Class 11 NCERT Notes