JNTU B.Tech IV ELECTRONIC MEASURING INSTRUMENTS Previous Question Paper (September - 2020 - R16)

First, calculate the internal resistance of the voltmeter (R_v) at the 100V scale: R_v = Sensitivity × Range = 15 kΩ/V × 100 V = 1.5 MΩ. When the voltmeter is connected across the unknown resistance R_x, the measured voltage V_m is 80 V and the current I is 1.8 mA. The resistance of the parallel combination of R_x and R_v is R_p = V_m / I = 80 V / 0.0018 A = 44.44 kΩ. Using the parallel resistance formula, 1/R_p = 1/R_x + 1/R_v, we find 1/R_x = 1/44.44 kΩ - 1/1500 kΩ = 0.0225 - 0.000667 = 0.021833 kΩ^-1, which gives R_x = 45.80 kΩ. The true voltage V_t across R_x (if the voltmeter were ideal) would be V_t = I × R_x = 0.0018 A × 45.80 kΩ = 82.44 V. The error due to the loading effect is V_m - V_t = 80 V - 82.44 V = -2.44 V. The percentage error is (-2.44 / 82.44) × 100 = -2.96%.

The Permanent Magnet Moving Coil (PMMC) instrument operates on the principle of electromagnetic torque. When a current flows through a coil placed in a uniform magnetic field, a mechanical force is exerted on the coil conductors.

The force on a conductor is given by F = BIl, where B is the flux density, I is the current, and l is the length of the conductor. For a coil with N turns and width d, the total deflecting torque T_d is:

where A = l × d is the area of the coil. Since B, N, and A are constants, T_d is directly proportional to the current I (T_d ∝ I).

The control torque T_c is provided by hairsprings, where T_c = kθ, with k being the spring constant and θ the deflection angle. At equilibrium, T_d = T_c, leading to:

This linear relationship between the deflection angle θ and the current I results in a uniform scale, which is a primary advantage of the PMMC movement.