If you've ever wondered about how batteries work, you might have heard the terms 'emf' and 'internal resistance'. Emf is basically the potential difference of a battery when there's no current flowing through it. On the other hand, internal resistance is the resistance that current faces while flowing through the battery itself. But, how do we actually figure out these values? Keep reading to find out. And remember, understanding emf and internal resistance is key to understanding how batteries work!

What is emf in electric circuits?

In simple terms, a voltage source creates a potential difference. This potential difference creates an electric field that produces a force, allowing current to flow through a circuit with resistance.

But what is emf? Despite its name, it's not exactly a force. Emf is a unique type of potential difference that's measured in volts (V). It's the potential difference of a source when no current is flowing through it. We can also define emf as the work done per unit charge.

Let's use a battery as an example. When a battery supplies current, the voltage across its terminals is less than the emf. As the battery depletes, this voltage level decreases. Once the battery is fully depleted and no longer supplies current, the voltage across its terminals will be equal to the emf.

Remember that all voltage sources produce emf, and understanding it is crucial in understanding how batteries work!

How do we calculate emf?

If you're curious about how to calculate emf, it can be done using the equation below:

Here, E stands for electrical energy in joules (J), and Q is the charge in coulombs (C).

However, it's important to note that the potential difference is called the terminal potential difference, and it will only be equal to the emf if there is no internal resistance. Unfortunately, real power supplies always have some internal resistance. Lost volts refer to the energy spent per coulomb while overcoming this internal resistance.

But don't worry - even with internal resistance, the conservation of energy still holds true in electric circuits.

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Lost volts is the name given to the energy spent per coulomb while overcoming the internal resistance. Also, be sure to check out our explanation on Energy Conservation.

What is internal resistance in electric circuits?

Load resistance is the total resistance of the components in an external electric circuit, while internal resistance is the resistance within the power source that resists current flow. Internal resistance can cause the power source to generate heat, as it is the opposition to the flow of current within the power source. This opposition results in a decrease in voltage, and the energy lost due to the opposition is converted to heat.

Measuring the internal resistance

Ohm's law states that V = I * R, where V is the voltage in volts, I is the current in amperes, and R is the external resistance in ohms. However, if we include the internal resistance, the total resistance will be R+r, where r is the internal resistance.

In this case, the voltage can be expressed as emf (ε). Expanding the brackets, we get V = I(R+r) = IR + Ir, where IR is the terminal potential difference in volts, and Ir is the volts, in voltsWe can rearrange the equation to get IR = emf - Ir, or VR = emf - Vr, where VR is the terminal potential difference, and Vr is the lost volts.

This relationship shows that if there is no internal resistance (and therefore, no lost volts), the terminal resistance will be equal to the emf. However, in most real-life situations, there is internal resistance, which causes the terminal potential difference to be less than the emf.

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Here are the solutions to the equations you provided:

Example 1:
Emf (ε) = 0.28V
Internal resistance (r) = 0.65Ω
Current (I) = 7.8mA

Using the equation VR = ε - Ir, we can calculate the terminal potential difference (VR):
VR = 0.28V - (0.65Ω * 7.8mA)
VR = 0.28V - 0.00507V
VR = 0.27493V

Therefore, the terminal potential difference is 0.27493V.

Example 2:
Current (I) = 0.45A
Internal resistance (r) = 0.25Ω

Using the equation P = I^2 * R, we can calculate the power dissipated in the internal resistance:
P = I^2 * r
P = (0.45A)^2 * 0.25Ω
P = 0.05625W

Since power is energy per second, the energy wasted per second (E) is equal to the power:
E = P
E = 0.05625J/s
E = 0.05625J

Therefore, the energy wasted per second on the internal resistance is 0.05625J.

Example 3:
Emf (ε) = 0.35V
Current (I) = 0.03A
Load resistance (R) = 1.2Ω

Using the equation VR = ε - IR, we can calculate the terminal potential difference (VR):
VR = 0.35V - (0.03A * 1.2Ω)
VR = 0.35V - 0.036V
VR = 0.314V

Using the equation R = (ε - VR) / I, we can calculate the internal resistance (r):
r = (ε - VR) / I - R
r = (0.35V - 0.314V) / 0.03A - 1.2Ω
r = 0.036V / 0.03A - 1.2Ω
r = 1.2Ω

Therefore, the internal resistance of the battery is 1.2Ω.

Emf and Internal Resistance - Key takeaways Electromotive force is not exactly a force: it is a unique kind of potential difference and is measured in volts. If there is no current, the voltage across the terminals of the voltage source will be equal to the emf. Lost volts is the given name for the energy spent per coulomb while overcoming the internal resistance. Internal resistance is the resistance within the power source that resists current flow and generally causes the power source to generate heat. The internal resistance of a voltage source depends on a variety of conditions, including how much it has been used, the size of the voltage source, the magnitude, and the direction of the current flowing through the voltage source.

Emf and Internal Resistance

How do determine the emf and internal resistance of an electrical cell?

By using the following equation, you can determine the emf and internal resistance of an electrical cell. The equation that describes the relation between emf, terminal voltage, and internal resistance is ε = VR + Vr, where ε is emf in volts, VR is the terminal voltage in volts, I is current in amperes, and r is the internal resistance in ohms. 

How do you calculate efficiency with emf and internal resistance?

Calculating the internal resistance of a source is an important factor in achieving optimum efficiency and getting the source to provide maximum power to the electric circuit. By using the following equation, you can calculate efficiency with emf and internal resistance. The equation that describes the relation between emf, terminal voltage, and internal resistance is ε = VR + Vr, where ε is emf in volts, VR is the terminal voltage in volts, I is current in amperes, and r is the internal resistance in ohms. 

How do you draw the emf and internal resistance graph gradient?

If you draw a graph that has the terminal potential difference on the y-axis and the circuit's current on the x-axis, you will obtain a straight line that has a negative gradient. The emf is then the intercept on the y-axis and the gradient represents r, the internal resistance. 

What are the emf and internal resistance of a battery?

Emf is the potential difference of the source when there is no current flowing through it, and internal resistance is the resistance within the power source that resists current flow.

Why is measuring the emf and internal resistance of a source important?

It is important to know the emf and internal resistance values of a source in order to determine how to get the source to provide maximum power to an electric circuit.

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