
Concept explainers
For the resistive element in Fig. 15.81:
- Write the current in phasor form.
- Calculate the voltage across the resistor in phasor form.
- Sketch the phasor diagram of the voltage and current.
- Write the voltage in the sinusoidal format.
- Sketch the waveform of the voltage and current.
Fig. 15.81

(a)
The Current in phasor form.
Answer to Problem 1P
The current in phasor form is
Explanation of Solution
Given:
The sinusoidal expression of current is
The resistor value is
Concept Used:
In resistive element network, the network consists of only resistor element.
Resistor does not have any phase angle. It's purely real.
In this, the network current is in phase with voltage.
Total impedance
Current:
Calculation:
In order to convert to phasor form
Conclusion:
Hence, the current in phasor form is

(b)
Voltage across resistor in phasor form.
Answer to Problem 1P
Voltage across resistor in phasor form is
Explanation of Solution
Given:
The sinusoidal expression of current is
The resistor value is
Concept Used:
In resistive element network, the network consists of only resistor element.
Resistor does not have any phase angle. It's purely real.
In this network current are in phase with voltage.
Total impedance
Current:
Calculation:
We know that voltage across resistor is given by
Conclusion:
Hence, the voltage across resistor in phasor form is

(c)
Phasor diagram of the voltage and current.
Answer to Problem 1P
Phasor diagram of the voltage and current is drawn.
Explanation of Solution
Given:
The sinusoidal expression of current is
The resistor value is
Concept Used:
In resistive element network, the network consists of only resistor element.
Resistor does not have any phase angle. It's purely real.
In this, network current are in phase with voltage.
Total impedance
Current:
Calculation:
Based on the voltage and current value which is already obtained in above part the phasor diagram is drawn. From real axis the angle value is counted.
Conclusion:
Hence, the phasor diagram of the voltage and current is drawn.

(d)
Voltage in the sinusoidal expressions.
Answer to Problem 1P
Voltage in the sinusoidal expressions is
Explanation of Solution
Given:
The sinusoidal expression of current is
The resistor value is
Concept Used:
In resistive element network, the network consists of only resistor element.
Resistor does not have any phase angle. It's purely real.
In this, the network current is in phase with voltage.
Total impedance
Current:
Calculation:
In order to convert to sinusoidal form,
Conclusion:
Hence, voltage in the sinusoidal expressions is

(e)
Waveform of the voltage and current.
Answer to Problem 1P
Waveform of the voltage and current is drawn.
Explanation of Solution
Given:
The sinusoidal expression of current is
The resistor value is
Concept Used:
In resistive element network, the network consists of only resistor element.
Resistor does not have any phase angle. It's purely real.
In this, the network current is in phase with voltage.
Total impedance
Current:
Calculation:
Based on the voltage and current value which is already obtained in the above part, the waveform diagram is drawn. Here, A stands for amplitude.
Conclusion:
Hence, waveform of the voltage and current is drawn.
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