Figure 3.48 shows a permanent-magnet moving-coil ammeter. When current \((I)\) flows through the coil wound on the core, the core rotates by an angle proportional to the magnitude of the current that is indicated by the pointer on a scale. The core, with the coil, has a mass moment of inertia \(J_{0}\), the torsional spring constant is \(k_{t}\), and the torsional damper has a damping constant of \(c_{t}\).

Figure 3.48:-

The scale of the ammeter is calibrated such that when a direct current of magnitude 1 ampere is passed through the coil, the pointer indicates a current of 1 ampere. The meter has to be recalibrated for measuring the magnitude of alternating current. Determine the steady-state value of the current indicated by the pointer when an alternating current of magnitude 5 amperes and frequency \(50 \mathrm{~Hz}\) is passed through the coil. Assume \(J_{0}=0.001 \mathrm{~N}-\mathrm{m}^{2}, k_{t}=62.5 \mathrm{~N}-\mathrm{m} / \mathrm{rad}\), and \(c_{t}=0.5 \mathrm{~N}-\mathrm{m}-\mathrm{s} / \mathrm{rad}\).

Piston Connecting rod- Crank Counterweights Chassis Shock mounts FIGURE 3.46 Four-cylinder automobile engine. Engine block