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In a AC circuit, resistive and total impedance are 10 and 20 ohms respectively. What is the phase angle difference between the voltage and current?
- a)0 degree
- b)30 degree
- c)45 degree
- d)60 degree
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In a AC circuit, resistive and total impedance are 10 and 20 ohms resp...
Cosɸ = R/Z; where R= 10 ohms and Z = 20 ohms than Cosɸ = 1/2 means phase angle is 60 degree.
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In a AC circuit, resistive and total impedance are 10 and 20 ohms resp...
**Explanation:**
**Impedance in an AC circuit:**
In an AC circuit, the impedance is the total opposition to the flow of current. It consists of two components: resistive impedance (R) and reactive impedance (X). The resistive impedance is purely resistive and represents the resistance in the circuit. The reactive impedance is either inductive (XL) or capacitive (XC) and represents the reactance in the circuit.
**Phase Angle Difference:**
The phase angle difference in an AC circuit is the phase shift between the voltage and current waveforms. It is denoted by the symbol φ (phi) and is measured in degrees or radians. The phase angle difference determines the relationship between voltage and current in an AC circuit.
**Given Data:**
- Resistive Impedance (R) = 10 ohms
- Total Impedance (Z) = 20 ohms
**Calculating the Reactive Impedance:**
To find the reactive impedance, we can use the following formula:
Z^2 = R^2 + X^2
Substituting the given values:
20^2 = 10^2 + X^2
400 = 100 + X^2
X^2 = 400 - 100
X^2 = 300
X = √300
X ≈ 17.32 ohms
**Calculating the Phase Angle Difference:**
The phase angle difference (φ) can be calculated using the following formula:
tan(φ) = X / R
tan(φ) = 17.32 / 10
φ = atan(17.32 / 10)
φ ≈ 60 degrees
Therefore, the phase angle difference between the voltage and current in the AC circuit is approximately 60 degrees. Hence, option D is the correct answer.
Note: The phase angle difference can also be calculated using other trigonometric functions such as cosine or sine, depending on the known quantities in the circuit.
**Impedance in an AC circuit:**
In an AC circuit, the impedance is the total opposition to the flow of current. It consists of two components: resistive impedance (R) and reactive impedance (X). The resistive impedance is purely resistive and represents the resistance in the circuit. The reactive impedance is either inductive (XL) or capacitive (XC) and represents the reactance in the circuit.
**Phase Angle Difference:**
The phase angle difference in an AC circuit is the phase shift between the voltage and current waveforms. It is denoted by the symbol φ (phi) and is measured in degrees or radians. The phase angle difference determines the relationship between voltage and current in an AC circuit.
**Given Data:**
- Resistive Impedance (R) = 10 ohms
- Total Impedance (Z) = 20 ohms
**Calculating the Reactive Impedance:**
To find the reactive impedance, we can use the following formula:
Z^2 = R^2 + X^2
Substituting the given values:
20^2 = 10^2 + X^2
400 = 100 + X^2
X^2 = 400 - 100
X^2 = 300
X = √300
X ≈ 17.32 ohms
**Calculating the Phase Angle Difference:**
The phase angle difference (φ) can be calculated using the following formula:
tan(φ) = X / R
tan(φ) = 17.32 / 10
φ = atan(17.32 / 10)
φ ≈ 60 degrees
Therefore, the phase angle difference between the voltage and current in the AC circuit is approximately 60 degrees. Hence, option D is the correct answer.
Note: The phase angle difference can also be calculated using other trigonometric functions such as cosine or sine, depending on the known quantities in the circuit.
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