Animated Solution for Physics - Magnetic Effects of Current: An ammeter reads upto 1 A. Its internal resistance is $0.81\Omega$. To increase the range to 10 A, the value of the required shunt is

The Magic of Shunt Resistors

Imagine you have a delicate measuring instrument, an ammeter, designed to safely measure a maximum current of $1\text{A}$. This is its full-scale deflection current, denoted as $I_g$. But what if you are faced with a circuit where a massive $10\text{A}$ current is flowing? If you were to connect your delicate $1\text{A}$ ammeter directly into this circuit, the excessive current would instantly fry its internal coil.

So, how do we measure this $10\text{A}$ current without destroying our instrument? The answer lies in creating a clever electrical bypass.

To protect the ammeter, we provide an alternate path for the excess current to flow. We do this by connecting a resistor in parallel with the ammeter. This parallel resistor is called a shunt resistor ($R$).

When the total current $I=10\text{A}$ reaches the junction before the ammeter, it splits into two paths. A small, safe portion of the current ($I_g=1\text{A}$) flows through the ammeter, causing it to show a full-scale deflection. The rest of the current, which we will call the shunt current ($I_s$), takes the bypass route through the shunt resistor.

According to Kirchhoff's Current Law (KCL), the total current entering a junction must equal the total current leaving it. Therefore, the current flowing through the shunt is simply the total current minus the current flowing through the ammeter:

Substituting our known values:

Now, we apply a fundamental principle of parallel circuits: the potential difference (voltage) across components connected in parallel is exactly the same. Therefore, the voltage drop across the shunt resistor must equal the voltage drop across the ammeter's internal resistance ($R_A$).

Using Ohm's Law ($V=IR$), we can write this relationship as:

We know that the ammeter's internal resistance $R_A$ is $0.81\Omega$. Let's plug all our values into the voltage equation:

Now, it is just a matter of simple algebra to isolate $R$:

By connecting a very small resistance of $0.09\Omega$ in parallel, we have successfully upgraded our $1\text{A}$ ammeter to safely measure up to $10\text{A}$.

Notice how small the shunt resistance is compared to the ammeter's internal resistance. This is intentional! A smaller resistance draws more current, effectively protecting the sensitive galvanometer coil. Furthermore, adding a parallel resistor decreases the overall equivalent resistance of the device, bringing it closer to the behavior of an ideal ammeter, which should have zero resistance.