AC Through Pure Ohmic Resistance

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Questions and Answers

What is the relationship between voltage and current in a purely ohmic circuit?

Voltage and current are in phase with each other. (correct)
Voltage leads current by 90 degrees.
Current leads voltage by 90 degrees.
Voltage and current are out of phase.

What is the maximum current 'I_m' in terms of the maximum voltage 'V_m' and resistance 'R'?

$I_m = V_m R$
$I_m = V_m + R$
$I_m = rac{V_m}{R}$ (correct)
$I_m = R V_m$

What does the equation $v = iR$ represent in an alternating current circuit?

Power calculation for resistive circuits.
The equilibrium of voltage and current across the resistor. (correct)
The applied voltage across an inductor.
The impedance of the circuit.

At what point does the instantaneous current ‘i’ reach its maximum value?

<p>When $sin heta$ is maximum, i.e., unity. (D)</p> Signup and view all the answers

Which of the following is NOT true about the alternating voltage and current waveforms in an ohmic resistor?

<p>The voltage waveform leads the current waveform. (D)</p> Signup and view all the answers

Flashcards

Voltage drop across a resistor

The instantaneous voltage across a resistor is equal to the product of the instantaneous current through the resistor and the resistance value.

Maximum current in a resistive circuit

The maximum value of the alternating current in a circuit with pure ohmic resistance is equal to the maximum value of the alternating voltage divided by the resistance.

Phase relationship in a resistive circuit

The alternating voltage and current waveforms in a purely resistive circuit are in phase with each other, meaning they reach their maximum and minimum values simultaneously.

Current-voltage relationship in a resistive circuit

The current in a circuit with only ohmic resistance is directly proportional to the applied voltage. This means that if the voltage doubles, the current also doubles.

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Power dissipation in a resistor

The power dissipated by a resistor is equal to the product of the voltage across the resistor and the current flowing through it.

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Study Notes

A.C. Through Pure Ohmic Resistance

The applied voltage is given by the equation: v = Vm sin ωt
Let R be the ohmic resistance, and i be the instantaneous current.
For equilibrium, the applied voltage must supply the ohmic voltage drop only, so v = iR
Substituting v into the equation, we get Vm sin ωt = iR. This gives us i = Vm sin ωt / R.
The current 'i' is maximum when sin ωt is unity. The maximum current (Im) is Vm / R.
Therefore, the current equation becomes i = Im sin ωt
Comparing the equations for voltage and current, we find voltage and current are in phase.
This is shown graphically in the figure. The voltage and current waveforms are directly aligned.
This is also illustrated vectorially in the figure, where the voltage vector (VR) and the current vector (I) are aligned (in phase).