Draw the circuit for experimental verification of Ohm's law using a source of variable DC voltage, a

Q: Why can't we just use the galvanometers directly without adding the extra resistors?

A galvanometer is highly sensitive and has a moderate resistance. If used directly in series, its resistance would alter the circuit's current. If used in parallel, it would draw too much current and likely burn out. The extra resistors calibrate its range and protect it.

Q: What would happen if I accidentally swapped the positions of the ammeter and voltmeter?

If the voltmeter is in series, its massive $10^6\ \Omega$ resistance would choke the circuit, reducing the current to almost zero. If the ammeter is in parallel, its tiny $10^{-3}\ \Omega$ resistance would create a short circuit, causing a massive current spike that could damage the instruments.

Q: Why do we need a variable DC voltage source instead of a fixed battery?

To verify Ohm's law ($V = IR$), you need to prove that the ratio of $V$ to $I$ is constant. A single reading isn't enough. A variable source allows you to take multiple readings at different voltages to plot a graph and confirm the linear relationship.

Q: Does the voltmeter measure the exact voltage across the $100\ \Omega$ resistor?

Practically, it measures a value extremely close to the exact voltage. Because the voltmeter has a finite (though very large) resistance of $10^6\ \Omega$, it draws a microscopic amount of current, causing a tiny measurement error. However, for most experiments, this error is negligible.

Q: Why is the shunt resistance so incredibly small ($10^{-3}\ \Omega$)?

The shunt must have a resistance much lower than the galvanometer itself. This ensures that almost all the current bypasses the sensitive galvanometer coil, allowing the ammeter to measure large currents without burning out or adding significant resistance to the main circuit.

Question

Draw the circuit for experimental verification of Ohm's law using a source of variable DC voltage, a main resistance of $100\ \Omega$, two galvanometers and two resistances of values $10^6\ \Omega$ and $10^{-3}\ \Omega$ respectively. Clearly show the positions of the voltmeter and the ammeter.

Sigma Percentile · Accepted Answer

### The Essence of Ohm's Law

Imagine you are trying to understand the flow of a river. To truly grasp its behavior, you need to measure two things: the volume of water flowing past a point (the current) and the difference in elevation driving that flow (the potential difference). Ohm's law is the electrical equivalent of this concept. It states that the current flowing through a conductor is directly proportional to the potential difference across it, provided the physical conditions remain constant.

To verify this beautiful relationship experimentally, we need a setup that allows us to measure both the current and the voltage across a known resistance while varying the power supplied. This requires three key components: a variable DC voltage source, an ammeter, and a voltmeter.

### Crafting the Perfect Ammeter

An ammeter's job is to count the electrons flowing through the circuit. To do this accurately, it must be placed directly in the path of the flow—in series. However, there is a catch. If the ammeter has a high resistance, it will act like a dam, restricting the flow and altering the very current it is trying to measure!

Therefore, an ideal ammeter must have zero resistance. In reality, we construct one by taking a sensitive galvanometer, $G_1$, and providing a bypass lane for the current. We connect a minuscule resistance—in this case, $10^{-3}\ \Omega$—in parallel with the galvanometer. This bypass lane is called a **shunt**. It allows the vast majority of the current to pass through unimpeded, while a tiny, proportional fraction goes through the galvanometer to give a reading.

### Designing the Voltmeter

While the ammeter measures the flow, the voltmeter measures the "electrical pressure" or potential difference across a component. To measure this difference, the voltmeter must be connected across the component—in parallel.

But here lies another challenge. If the voltmeter has a low resistance, it will create a new path for the current, drawing electrons away from the main circuit and giving a false reading. An ideal voltmeter should be like a pressure gauge that doesn't let any water leak out; it must have infinite resistance. We achieve this practically by taking our second galvanometer, $G_2$, and connecting a massive resistance—here, $10^6\ \Omega$—in series with it. This ensures that only a negligible trickle of current passes through the voltmeter, keeping the main circuit undisturbed.

### Assembling the Master Circuit

Now, we bring all the pieces together to form our experimental setup. We place our main resistance of $100\ \Omega$ in the center of the circuit.

First, we connect our newly crafted ammeter in **series** with the $100\ \Omega$ resistance. This ensures that whatever current flows through the main resistance also flows through the ammeter.

Next, we connect our voltmeter in **parallel** across the $100\ \Omega$ resistance. This allows the voltmeter to "feel" the exact potential difference across the ends of the resistor.

Finally, we connect the variable DC voltage source to power the entire setup. By adjusting the voltage source, we can change the current in the circuit. For each setting, we record the current $I$ from the ammeter and the voltage $V$ from the voltmeter. Plotting these values will yield a straight line passing through the origin, triumphantly verifying Ohm's law!

Visualized Solution

$V = I R$

$R_{amm e t er} \approx 0$

$R_{v o l t m e t er} \approx \infty$

$C i r c u i t A sse mb l y$

The Sigma Insight: Electrical Instruments

The Essence of Ohm's Law

Crafting the Perfect Ammeter

Designing the Voltmeter

Assembling the Master Circuit

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