Moving-Coil Galvanometer (MCG) 🧲

Why we love it 🤔

Need to know if I really flows or how big the voltage drop is? The MCG turns invisible currents into visible twists of a pointer. Simple, clever, and perfect for lab work! :contentReference[oaicite:0]{index=0}

Construction 🛠️

  • A light rectangular coil with N turns can spin freely about a fixed axis inside a uniform radial magnetic field. A cylindrical soft-iron core keeps the field radial ➕ boosts its strength. :contentReference[oaicite:1]{index=1}
  • A hair-spring provides restoring torque and carries current to the coil. :contentReference[oaicite:2]{index=2}
  • A pointer on the coil sweeps over a scale so you can read the deflection easily. :contentReference[oaicite:3]{index=3}

Principle 🌟

  • Magnetic torque on the coil:
    $$\tau = NIAB$$
    (we take $$\sin\theta = 1$$ thanks to the radial field) :contentReference[oaicite:4]{index=4}
  • Spring torque tries to pull it back: $$k\phi$$. At equilibrium:
    $$k\phi = NIAB$$
    so deflection is
    $$\displaystyle \phi = \frac{NAB}{k}\,I \tag{4.26}$$ :contentReference[oaicite:5]{index=5}

Using it as a detector 🔍

With no current, the pointer rests mid-scale. Current to the right? Pointer swings right. Current reversed? It swings left. Easy! :contentReference[oaicite:6]{index=6}

Why it can’t be an ammeter by itself ❌

  1. Super-sensitive: full-scale deflection happens with microampere currents. :contentReference[oaicite:7]{index=7}
  2. High internal resistance RG; placing it in series would change the very current you want to measure. :contentReference[oaicite:8]{index=8}

Conversion to Ammeter 🔄

  • Put a tiny shunt rs in parallel with the coil so most current bypasses the meter. :contentReference[oaicite:9]{index=9}
  • Effective resistance becomes $$R \approx r_s$$ when $$R_G \gg r_s$$ — almost no disturbance to the circuit. :contentReference[oaicite:10]{index=10}
  • Current sensitivity (deflection per ampere):
    $$\displaystyle \frac{\phi}{I} = \frac{NAB}{k} \tag{4.27}$$ :contentReference[oaicite:11]{index=11}
  • Want more sensitivity? Add more turns N 🚀 (within practical limits). :contentReference[oaicite:12]{index=12}

Conversion to Voltmeter 🔋

  • Put a large series resistor R with the coil and connect the pair across the component. Now the combo draws only a tiny fraction (<1 %) of circuit current. :contentReference[oaicite:13]{index=13}
  • Total resistance is $$R_G + R \approx R$$ (huge). :contentReference[oaicite:14]{index=14}
  • Voltage sensitivity (deflection per volt):
    $$\displaystyle \frac{\phi}{V} = \frac{NAB}{kR} \tag{4.28}$$ :contentReference[oaicite:15]{index=15}
  • Doubling turns doubles $$R_G$$ too, so voltage sensitivity stays roughly the same — a classic exam trick! 🚧 :contentReference[oaicite:16]{index=16}

Quick Worked Example 🧮

A coil with $$R_G = 60\ \Omega$$ in a 3 Ω circuit shows only 0.048 A. Add a 0.02 Ω shunt and the reading jumps to 0.99 A, almost matching the ideal 1.00 A. Perfect demo of why the shunt matters! :contentReference[oaicite:17]{index=17}

High-Yield Ideas for NEET ✅

  1. Torque-deflection law $$\phi = (NAB/k)\,I$$ and what each symbol means. 🧲
  2. Shunt trick for ammeters: $$R \approx r_s$$ when $$R_G \gg r_s$$. ⚡
  3. Series resistor trick for voltmeters and voltage sensitivity $$\phi/V = NAB/(kR)$$. 🔋
  4. Current sensitivity rises with more turns, but voltage sensitivity does not—watch for that! 📈
  5. Why an MCG alone can’t measure big currents (high resistance ➕ µA full-scale). 🚀