Analog Electronics: Chapter 6 - Understanding Electric Potential and Voltage

In the world of analog electronics, everything begins with charges and the fields they create.

To truly understand voltage — the backbone of every circuit — we must first understand what electric potential means.

🔹 What is Electric Potential?

Every charge in nature, called a source charge (Q), produces an electric field around it. This field extends theoretically up to infinity, though it becomes weaker as we move farther away.

Now, imagine bringing a very small positive test charge into this electric field.

If this test charge starts from infinity — a point so far away that the source charge’s field is negligible — the electric potential at infinity is taken as zero.

When you move the test charge from infinity to a point at distance R from the source charge, you must do work against the field (if the source charge is positive). This work done per unit positive charge in bringing the test charge from infinity to that point is called the electric potential at that point.

Mathematically,

where
V = electric potential (in volts),
W = work done (in joules), and
q = test charge (in coulombs).

🔹 Conceptual Understanding

If the source charge is positive, a positive test charge will be repelled by it.
To move it closer, you must apply an external force — this effort (work) gets stored as electric potential energy.

Thus, electric potential at a point tells us how much work per unit charge is required to bring a positive test charge from infinity to that point in the source’s electric field.

⚙️ Example Setup

Let’s make this more concrete with a simple example:

1. Setup:

• You have a source charge Q.
• It produces an electric field around it.
• You bring a test charge from infinity to a point A.

Suppose the work done per unit charge (from infinity to A) = 12 V
→ Electric potential at point A, VA = 12V.

• Now, move the test charge even closer to a new point B.
  Work done per unit charge (from infinity to B) = 14 V
  → Electric potential at point B, VB = 14V.

🔹 Voltage (Potential Difference)

The voltage or potential difference between two points tells us how much extra work per unit charge is needed to move a test charge from one point to another.

Mathematically,

Substituting the values:

This means the potential difference between B and A is 2 volts.

🧠 Interpreting the Result

• Electric potential at A (12 V):
  Energy required per coulomb to bring the test charge from infinity to point A.
• Electric potential at B (14 V):
  Energy required per coulomb to bring the test charge from infinity to point B.
• Voltage (2V between A and B):
  Additional 2 joules of work are needed to move 1 coulomb of charge from A to B.

✅ In words:
If it takes 12 V to bring a charge from infinity to A, and 14 V to bring it from infinity to B, then the potential difference between B and A is 2 V.
You must perform an additional 2 J of work per coulomb to move the charge from A to B.

⚡ Additional Concept: Effect of Charge on Potential

The electric potential at any point doesn’t depend only on distance — it also depends on how much charge is present at the source.
If we have two different source charges, say Qₐ and Qᵦ, where Qₐ > Qᵦ, then the point around Qₐ will have a higher potential than the same point around Qᵦ.

This happens because a larger charge produces a stronger electric field, which exerts a greater force on any test charge placed near it.
To move a test charge in this stronger field, more work must be done per unit charge to bring it from infinity to that point — and this extra work shows up as higher potential.

Remember,

Since the force between charges increases with the amount of charge and decreases with distance, the work done (and therefore potential) also depends on these two factors.

So, when we compare two points around different charges, the one near the stronger charge will always have higher potential, because it takes more energy per unit charge to reach that region.

🔹 Summary

• Electric Potential (V):
  Work done per unit positive charge to bring it from infinity to a point in an electric field (without acceleration).

• Voltage / Potential Difference (V_AB):
  Difference in electric potentials between two points.

It tells how much work per coulomb is required to move a charge between those two points in an electric field.

🔸 Analogy to Circuits

In a circuit, the same concept applies:

• Voltage is like the “push” that drives charges (electrons) to move through a conductor.
• Just as height difference makes water flow, potential difference makes current flow.

That’s why we often say:

“Current flows because of voltage difference.”

✨ Conclusion

Electric potential gives us a sense of how much energy is stored per charge at a point in an electric field, while voltage tells us the difference in that energy between two points.

Understanding this concept is foundational — it connects physics to circuit theory and sets the stage for analyzing analog systems like resistors, capacitors, and transistors in upcoming chapters.