4.10. THE MOVING COIL GALVANOMETER

Currents and voltages in circuits have been discussed extensively in Chapters 3. But how do we measure them? How do we claim that current in a circuit is 1.5 A or the voltage drop across a resistor is 1.2 V? Figure 4.20 exhibits a very useful instrument for this purpose: the moving coil galvanometer (MCG).

The moving coil galvanometer is an instrument designed to measure electric currents and voltages in circuits. It operates on the principle of electromagnetism—specifically, the interaction between magnetic fields and electric currents. By detecting the angular deflection of a coil in a magnetic field due to the flow of current, it provides an indication of the current's magnitude.

Think of the galvanometer like a measuring stick used to gauge the amount of fluid in a container. Just as a measuring stick can tell you how much fluid is present based on its level, a galvanometer indicates the strength of an electric current based on how much the coil moves in response to it.

The galvanometer consists of a coil, with many turns, free to rotate about a fixed axis, in a uniform radial magnetic field. There is a cylindrical soft iron core which not only makes the field radial but also increases the strength of the magnetic field.

The moving coil galvanometer features a coil composed of multiple turns of wire, allowing for significant electromagnetic induction. When a current flows through this coil, it generates a magnetic field. Meanwhile, the external uniform magnetic field interacts with this coil, producing a torque that causes the coil to rotate. This rotation is proportional to the current flowing through the coil.

Imagine spinning a bicycle wheel. The spokes of the wheel represent the loops of wire in the galvanometer. When the wheel turns, it shows how fast you're going, just like the rotating coil of the galvanometer indicates the strength of the current.

When a current flows through the coil, a torque acts on it. This torque is given by Eq. (4.20) to be τ = NIAB where the symbols have their usual meaning. Since the field is radial by design, we have taken sin θ = 1 in the above expression for the torque.

When current flows through the coil, it experiences torque, which is the rotational force acting on it. The torque can be calculated using the formula τ = NIAB, where N is the number of turns, I is the current, A is the area of the coil, and B is the strength of the magnetic field. Since the magnetic field is designed to be uniform and radial, the angle θ is effectively 90 degrees, making sin θ equal to 1.

Consider opening a door. The torque you apply to the door handles when you push on it affects how far the door swings open. Similarly, the electric current creates a 'push' (torque) on the coil, which makes it 'swing' (rotate) to indicate the current value.

A spring S provides a counter torque kφ that balances the magnetic torque NIAB; resulting in a steady angular deflection φ. In equilibrium kφ = NI AB.

To achieve a stable reading, the galvanometer incorporates a spring that counteracts the torque from the magnetic field acting on the coil. As the coil rotates due to current, a balance is established when the torsional force exerted by the spring (kφ) equals the torque produced by the current in the coil (NIAB). This is known as the equilibrium position where the needle points to a definitive current value on the scale.

Think of a seesaw with weights on either side. If one side is heavier, the seesaw tips, but if you add enough weight on the lighter side, it can balance out. The spring in the galvanometer acts like the weight that balances the seesaw, ensuring the reading remains stable.

The galvanometer cannot as such be used as an ammeter to measure the value of the current in a given circuit. This is for two reasons: (i) Galvanometer is a very sensitive device, it gives a full-scale deflection for a current of the order of µA. (ii) For measuring currents, the galvanometer has to be connected in series, and as it has a large resistance, this will change the value of the current in the circuit.

While the galvanometer provides accurate readings for very small currents, it is not practical as an ammeter because it cannot handle larger currents effectively. Due to its sensitivity, connecting it directly to a circuit can cause it to exceed its operational limits, leading to inaccurate measurements.

Consider a tiny scale designed to weigh small pearls. If you tried to place a bucket of sand on it, it would be overwhelmed and probably break. Similarly, the galvanometer is excellent for fine measurements, but it can't simply be plugged directly into strong currents.

To overcome these difficulties, one attaches a small resistance r, called shunt resistance, in parallel with the galvanometer coil; so that most of the current passes through the shunt.

To convert the galvanometer into an effective ammeter, a shunt resistor is placed in parallel with the device. This design allows the majority of the current to bypass the galvanometer, ensuring that the sensitive instrument only measures a small, manageable fraction of the current in the circuit, thus preventing damage and ensuring accurate readings.

Imagine using a water flow valve to protect a delicate measuring cup in a pipeline. The valve allows most of the water to flow past safely while controlling the tiny amount that reaches the delicate cup, protecting it from overflow. Similarly, the shunt protects the galvanometer.

The galvanometer can also be used as a voltmeter to measure the voltage across a given section of the circuit. For this it must be connected in parallel with that section of the circuit.

The galvanometer can be adapted to measure voltage by connecting it in parallel with the circuit component across which the voltage is to be measured. This configuration allows the galvanometer to sense the potential difference while drawing minimal current to ensure it does not affect the circuit operations significantly.

Consider a fly landing on a scale. It will read the weight without significantly changing the weight of the object being measured. Similarly, when the galvanometer measures voltage, it takes a small 'sip' of current so that the overall circuit behavior remains mostly unchanged.

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