Question 513: Current Electricity

Question

Two identical galvanometers are converted into an ammeter and into milliammeter. For the same current, the value of shunt of the ammeter as compared to that of milliammeter is

Accepted Answer

We start with the fact that when converting a galvanometer (with full-scale deflection current $$I_g$$ and internal resistance $$R_g$$) into an ammeter, a shunt resistor is connected in parallel with the galvanometer. This shunt resistor is chosen so that when the instrument carries its full-scale current (say, $$I$$), only $$I_g$$ passes through the galvanometer and the balance, $$I - I_g$$, goes through the shunt. Since the voltage across both branches must be the same, we have
$$ I_g R_g = (I - I_g) R_s, $$
which gives
$$ R_s = \frac{I_g R_g}{I - I_g}. $$
LetÃ¢ÂÂs compare two cases:
For an ammeter (designed for high currents), let the fullÃ¢ÂÂscale reading be $$I_A$$. Then the required shunt is
$$    R_{sh,A} = \frac{I_g R_g}{I_A - I_g}.    $$
For a milliammeter (designed for measuring currents in the milliampere range), let the fullÃ¢ÂÂscale reading be $$I_m$$ (and here, $$I_m$$ is only slightly greater than $$I_g$$). Then the required shunt is
$$    R_{sh,m} = \frac{I_g R_g}{I_m - I_g}.    $$
Since an ammeter is meant for much larger currents, we typically have
$$ I_A \gg I_m. $$
Thus, the denominator in $$R_{sh,A}$$ becomes very large compared to that in $$R_{sh,m}$$. In effect,
$$ R_{sh,A} < R_{sh,m}. $$
In other words, for the same galvanometer (and hence the same $$I_g$$ and $$R_g$$) and for the same actual current through the instrument, the conversion of the galvanometer into an ammeter (with a high current range) requires a much smaller shunt resistor compared to the one used for converting it into a milliammeter.
So, the shunt of the ammeter is
less
than that of the milliammeter.
Answer: Option A (less).

Answer

less

Answer

equal

Answer

more

Answer

zero

Current Electricity

Two identical galvanometers are converted into an ammeter and into milliammeter. For the same current, the value of shunt of the ammeter as compared to that of milliammeter is

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