Animated Solution for Physics - Current Electricity: A microammeter has a resistance of $100\Omega$ and full scale range of $50\mu \text{A}$. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combination(s)

Imagine you have a highly sensitive instrument—a microammeter—that twitches its needle at the slightest whisper of electrical current. In our case, this galvanometer has a resistance of $100\Omega$ and reaches its maximum limit (full-scale deflection) at a mere $50\mu \text{A}$.

But what if you want to measure a roaring river of current, like $5\text{mA}$, or a substantial potential difference, like $10\text{V}$? You don't need to buy a new instrument; you just need to cleverly redirect the electricity. This is the beautiful art of shunts and multipliers.

Bypassing the Flood

To convert our delicate galvanometer into a robust ammeter, we must protect it from the excess current. We do this by providing an alternate, low-resistance path—a shunt ($S$)—connected in parallel.

When a large current $i$ enters the setup, only the safe amount $i_g$ goes through the galvanometer, while the rest $(i-i_g)$ rushes through the shunt. Because they are in parallel, the voltage drop across both paths is identical:

Rearranging this gives us our master equation for the shunt resistance:

Let's test Option (c), which proposes a $5\text{mA}$ range. Substituting our values:

Here is a pro-tip: $50\mu \text{A}$ is incredibly small compared to $5\text{mA}$ ($5000\mu \text{A}$). We can safely approximate the denominator to just $5000\mu \text{A}$.

A $1\Omega$ parallel resistance perfectly converts our instrument into a $5\text{mA}$ ammeter. Option (c) is correct!

Dropping the Pressure

Now, let's switch gears. What if we want to measure voltage? A voltmeter must be connected in parallel across a component, which means it will experience the full voltage. To prevent our sensitive galvanometer from frying, we must connect a massive resistance—a multiplier ($R$)—in series.

This high resistance ensures that even at the maximum voltage $V$, only the tiny full-scale current $i_g$ flows through the instrument. The total voltage is the sum of the voltage drops:

Rearranging for $R$, we get:

Let's evaluate Option (b), which suggests a $10\text{V}$ range. Plugging in the numbers:

In the practical world of electronics, $100\Omega$ is completely negligible when standing next to $200,000\Omega$. We can confidently round this to $200\text{k}\Omega$. Option (b) is also correct!

By mastering the principles of parallel and series circuits, we've unlocked the true versatility of the galvanometer. A tiny $1\Omega$ shunt turns it into a $5\text{mA}$ ammeter, while a massive $200\text{k}\Omega$ series resistor transforms it into a $10\text{V}$ voltmeter.