When 2 Amp current is passed through a tangent galvanometer....

When 2 Amp current is passed through a tangent galvanometer. It gives a deflection of $30^{\circ} .$ For $60^{\circ}$ deflection, the current must be
(a) $1 \mathrm{Amp}$
(b) $2 \sqrt{3 a m p}$
(c) $4 \mathrm{amp}$
(d) $6 \mathrm{Amp}$

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Key Concepts

Trigonometric Relationship in Magnetic Deflection

In a tangent galvanometer, the deflection angle of the needle is related to the magnetic field produced by the current through a trigonometric relationship, specifically the tangent function. The deflection angle (?) satisfies the relation tan(?) = (constant × I) / B, where I is the current and B is the earth's horizontal magnetic field. This relationship is key to determining unknown currents by measuring the angle of the needle.

Proportionality Principle in Measurement

Because the tangent function directly relates the deflection angle to the current in a tangent galvanometer, the current is proportional to tan(?). This means that if the deflection angle increases such that its tangent value increases by a certain factor, the current increases by the same factor. This proportionality allows for the calculation of new current values when the deflection angle is changed.

Tangent Galvanometer

A tangent galvanometer is an instrument used to measure electric currents by utilizing the magnetic field produced by the current. It consists of a coil of wire that, when carrying current, produces a magnetic field which interacts with the earth's magnetic field, causing a needle to deflect. The amount of deflection is indicative of the strength of the current flowing through the coil.

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