A Galvanometer has a resistance G and Q current IG flowing in it produces full scale deflection.

A Galvanometer has a resistance G and Q current IG flowing...

A Galvanometer has a resistance $\mathrm{G}$ and $\mathrm{Q}$ current $\mathrm{I}_{\mathrm{G}}$ flowing in it produces full scale deflection. $\mathrm{S}_{1}$ is the value of the shunt which converts it into an ammeter of range 0 to $\mathrm{I}$ and $\mathrm{S}_{2}$ is the value of the shunt for the range 0 to $2 \mathrm{I}$. The ratio $\left(\mathrm{S}_{1} / \mathrm{S}_{2}\right) \mathrm{is}$ (a) $\left[\left(2 \mathrm{I}-\mathrm{I}_{\mathrm{G}}\right) /\left(\mathrm{I}-\mathrm{I}_{\mathrm{G}}\right)\right]$ (b) $(1 / 2)\left[\left(\mathrm{I}-\mathrm{I}_{\mathrm{G}}\right) /\left(2 \mathrm{I}-\mathrm{I}_{\mathrm{G}}\right)\right]$ (c) 2 (d) 1

A Galvanometer has a resistance $\mathrm{G}$ and $\mathrm{Q}$ current $\mathrm{I}_{\mathrm{G}}$ flowing in it produces full scale deflection. $\mathrm{S}_{1}$ is the value of the shunt which converts it into an ammeter of range 0 to $\mathrm{I}$ and $\mathrm{S}_{2}$ is the value of the shunt for the range 0 to $2 \mathrm{I}$. The ratio $\left(\mathrm{S}_{1} / \mathrm{S}_{2}\right) \mathrm{is}$
(a) $\left[\left(2 \mathrm{I}-\mathrm{I}_{\mathrm{G}}\right) /\left(\mathrm{I}-\mathrm{I}_{\mathrm{G}}\right)\right]$
(b) $(1 / 2)\left[\left(\mathrm{I}-\mathrm{I}_{\mathrm{G}}\right) /\left(2 \mathrm{I}-\mathrm{I}_{\mathrm{G}}\right)\right]$
(c) 2
(d) 1

Key Concepts

Galvanometer

A galvanometer is a sensitive instrument used to detect and measure small currents. It displays current magnitude through a mechanical deflection, with the deflection being proportional to the magnitude of the current passing through it.

Shunt Resistor

A shunt resistor is a precise resistor used to bypass the bulk of a current intended for a delicate instrument like a galvanometer. By placing it in parallel with the galvanometer, the device can safely measure larger currents by diverting the excess current away from the sensitive mechanism.

Full-scale Deflection

Full-scale deflection refers to the maximum current a galvanometer can measure before its pointer reaches the limit of its scale. This parameter is critical when converting a galvanometer into an ammeter since the current through the galvanometer must not exceed this limit.

Ammeter Range Extension

Converting a galvanometer to an ammeter involves adding a shunt resistor so that only the maximum allowable current (full-scale deflection current) flows through the galvanometer, while the rest flows through the shunt. This allows the modified instrument to measure currents significantly larger than its inherent full-scale current.

Transcript

00:01 So in this problem, we're given two different scenarios with the same galvanometer.

00:05 So in the first, we have a volt meter, which has been connected to a 2 .5 kilo -oam resistor in order to have a full -scale deflection at 2 volts.

00:16 And in the second scenario, we have the galvanometer hooked up in parallel to a 0 .2 -oam resistor in order to create an ammeter with a full -scale deflection at 0 .5 amps.

00:29 So what we want to do is we want to find out what the internal resistance and and what current we need to get full -scale deflection of this galvanometer just by itself.

00:40 So in order to do this, we're going to use these two scenarios to set up two equations where we can then solve for the unknowns.

00:47 So if we look at this scenario first, the volt meter, we know that the voltage across these two resistors is going to be two volts.

00:59 And this voltage is going to be equal to the equivalent resistance, which is r plus 2 .5 kilo -ooms, times the current that's flowing through it, which will be ig, or the current that's needed to get full -scale deflection in the galvanometer.

01:20 So we have our first equation here, and we're going to go over to the m meter now, and we have these two branches in parallel, and we know that the voltage across them is going to be equal.

01:31 So again, we're going to use omslaw.

01:34 And we're first going to look at the top branch.

01:36 So we have r times ig, which is going to be equal to the voltage...

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