Animated Solution for Physics - Current Electricity: An energy source will supply a constant current into the load, if its internal resistance is

The heartbeat of every electrical circuit is its energy source. Whether it's a tiny AA battery powering a remote or a massive generator lighting up a city, understanding how these sources deliver current is fundamental to physics. Today, we are going to dive deep into a classic problem that tests our understanding of ideal energy sources, internal resistance, and Ohm's law.

Imagine you have a simple circuit. You have an energy source, let's say a battery, which has an electromotive force (EMF) denoted by $E$. However, no real-world battery is perfect. The materials inside the battery resist the flow of electrons to some extent. This inherent resistance is called the internal resistance, denoted by $r$.

We connect this battery to an external device, like a light bulb or a heater, which we call the load resistance, denoted by $R$. When the circuit is closed, a current $I$ begins to flow.

To find out exactly how much current is flowing, we turn to our trusty tool: Ohm's Law. The total resistance of this circuit is the sum of the external load and the internal resistance, which is $R+r$. Therefore, the current $I$ flowing through the circuit is given by the equation:

This equation is the master key to unlocking the behavior of the circuit. It tells us that the current depends on three things: the strength of the battery ($E$), the resistance of the load ($R$), and the internal resistance of the battery itself ($r$).

The question asks us for the condition under which the energy source will supply a constant current into the load. Let's look at our master equation again. If we want the current $I$ to be as steady and maximum as possible without any energy being wasted inside the battery itself, what should $r$ be?

If we set the internal resistance $r=0$, our equation simplifies beautifully to:

In this scenario, all the EMF $E$ is applied directly across the load $R$. There is no voltage drop inside the battery. Assuming the load $R$ is a fixed, constant value, the current $I$ will remain perfectly constant. An energy source with zero internal resistance is known as an ideal voltage source. Therefore, based on the provided solution logic for a fixed load, the internal resistance must be zero.

Ideal Current Source

Now, I must warn you about a very common trap! What if the load resistance $R$ is not fixed? What if it's a variable resistor? If $R$ changes, and $r=0$, the current $I=\frac{E}{R}$ will absolutely change!

In advanced circuit theory, if you want a source that delivers a constant current regardless of how much the load $R$ changes, you need an ideal current source. Mathematically, this happens when the internal resistance $r$ is infinitely large ($r\to \infty$). In that extreme case, the current is bottlenecked entirely by $r$, making $I\approx \frac{E}{r}$, which stays constant even if $R$ fluctuates.

However, in the context of standard introductory physics problems where the load is assumed to be a specific, fixed entity, the condition for delivering the full, unfluctuating current without internal power loss is having zero internal resistance. Always read the context of the problem carefully!