A galvanometer having a coil resistance of 100 Ωgives a full scale deflection, when a current of

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A galvanometer having a coil resistance of 100 Ωgives a full...

A galvanometer having a coil resistance of $100 \Omega$ gives a full scale deflection, when a current of $1 \mathrm{~mA}$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10 \mathrm{~A}$, is (A) $2 \Omega$ (B) $0.1 \Omega$ (C) $3 \Omega$ (D) $0.01 \Omega$

A galvanometer having a coil resistance of $100 \Omega$ gives a full scale deflection, when a current of $1 \mathrm{~mA}$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10 \mathrm{~A}$, is
(A) $2 \Omega$
(B) $0.1 \Omega$
(C) $3 \Omega$
(D) $0.01 \Omega$

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Key Concepts

Galvanometer

A galvanometer is an instrument that uses a fine moving coil in a magnetic field to detect and measure small currents. Its sensitivity is characterized by its full scale deflection current and internal (coil) resistance, which determine how easily it can be deflected by an electrical current.

Ammeter Conversion

Converting a galvanometer into an ammeter involves modifying the circuit so that the galvanometer, which can only handle very small currents, can measure much larger currents. This is achieved by adding a low-resistance shunt resistor in parallel with the galvanometer, which diverts most of the current away from it, allowing it to operate safely at its designed low current threshold while still indicating full scale deflection.

Shunt Resistor Calculation

The value of the shunt resistor is calculated based on the principle that the voltage drop across the galvanometer must equal the voltage drop across the shunt resistor. By setting the product of the galvanometer’s full scale current and its resistance equal to the product of the bypass current (the total desired current minus the galvanometer current) and the shunt resistor, one can derive the required low resistance value. This ensures that even when the total current is very high, only the safe, small fraction flows through the galvanometer.

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