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If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is t
If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)
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If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)
10Ω
30Ω
33.33Ω
40Ω
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Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.
Questions & Step-by-step Solutions
1 item
Q
Q: If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)
Solution:
Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.
Steps: 8
Show Steps
Step 1: Identify the resistance (R) and inductive reactance (XL) values. Here, R = 10Ω and XL = 30Ω.
Step 2: Write the formula for total impedance (Z): Z = √(R² + (XL)²).
Step 3: Substitute the values of R and XL into the formula: Z = √(10² + 30²).
Step 4: Calculate R²: 10² = 100.
Step 5: Calculate XL²: 30² = 900.
Step 6: Add the results from Step 4 and Step 5: 100 + 900 = 1000.
Step 7: Take the square root of the sum: Z = √1000.
Step 8: Calculate the square root: Z ≈ 31.62Ω.
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