A moving-coil meter has 100 turns, coil length 40 mm, coil width 30 mm, and a uniform flux density B = 1 Wb/m^2. If the control (restoring) torque at full-scale is 240 × 10^-6 N·m, what is the full-scale current range of the meter?

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Permanent-magnet moving-coil (PMMC) instruments balance electromagnetic deflecting torque against a spring control torque. At full-scale deflection, the two torques are equal, which allows the full-scale current to be determined from geometry and magnetic field data. This is a standard single-step substitution problem in electrical measurements. Given Data / Assumptions: Number of turns N = 100. Coil dimensions: length l = 0.04 m, width w = 0.03 m → area A = l * w = 0.0012 m^2. Flux density B = 1 Wb/m^2 (uniform in the air gap). Control torque at full scale T_c = 240 × 10^-6 N·m. At full-scale: deflecting torque T_d = control torque T_c. Concept / Approach:Deflecting torque for PMMC: T_d = N * B * I * A. Set T_d = T_c and solve for the full-scale current I_fs. This is simple algebra with consistent SI units. Step-by-Step Solution: Compute area A = 0.04 * 0.03 = 0.0012 m^2.Set N * B * I_fs * A = 240 × 10^-6.I_fs = (240 × 10^-6) / (100 * 1 * 0.0012) = 240 × 10^-6 / 0.12 = 2 × 10^-3 A.Therefore I_fs = 2 mA. Verification / Alternative check: Units: (Wb/m^2)(A)(m^2) = Wb·A, which in this torque relation reduces to N·m; dimensions are consistent. Why Other Options Are Wrong: 1 mA, 3 mA, and 4 mA do not satisfy the torque balance with the given parameters. Common Pitfalls: Forgetting to convert millimeters to meters or miscomputing the area. Final Answer: 2 mA

A moving-coil meter has 100 turns, coil length 40 mm, coil width 30 mm, and a uniform flux density B = 1 Wb/m^2. If the control (restoring) torque at full-scale is 240 × 10^-6 N·m, what is the full-scale current range of the meter?

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