A 50 Volt range spring controlled, electrodynamic voltmeter having a s...
Calculation of True Potential Difference across the Instrument
Given Parameters:
- Voltage Range (V) = 50V
- Full Scale Deflection (θ) = 900
- Current for Full Scale Deflection (I) = 0.05A
- Control Constant (K) = 0.5 x 10^-6 N-m/degree
- Initial Mutual Inductance (M) = 0.50H
- Frequency (f) = 50Hz
Calculation of Spring Constant (Ks):
The spring constant can be calculated using the formula:
Ks = (θ/2π) x (I^2 x M)/(V x K)
Substituting the given values, we get:
Ks = (900/2π) x (0.05^2 x 0.50)/(50 x 0.5 x 10^-6)
Ks = 318.3099 N/m
Calculation of Angular Frequency (ω):
Angular frequency can be calculated using the formula:
ω = 2πf
Substituting the given value of frequency, we get:
ω = 2 x 3.1416 x 50
ω = 314.16 rad/s
Calculation of Current (I1) at 50V:
At 50V, the deflection of the voltmeter is:
θ1 = (50/50) x 900 = 900
The current required for this deflection can be calculated using the formula:
I1 = (θ1/2π) x (V x K)/(M x Ks)
Substituting the given values, we get:
I1 = (900/2π) x (50 x 0.5 x 10^-6)/(0.50 x 318.3099)
I1 = 0.055A
Calculation of True Potential Difference:
The true potential difference can be calculated using the formula:
Vt = V x (I1/I)
Substituting the calculated values, we get:
Vt = 50 x (0.055/0.05)
Vt = 55V
Explanation:
A spring controlled, electrodynamic voltmeter operates on the principle of torque produced by the interaction of magnetic fields. The deflection of the voltmeter is proportional to the current flowing through it, and hence the potential difference can be measured. The spring provides the restoring torque, which is proportional to its spring constant. The control constant represents the torque produced by the interaction of magnetic fields, while the mutual inductance represents the coupling between the two