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Terminal potential difference and the potential divider IB DP Physics Study Notes

Terminal potential difference and the potential divider IB DP Physics Study Notes - 2025 Syllabus

Terminal potential difference and the potential divider IB DP Physics Study Notes

Terminal potential difference and the potential divider IB DP Physics Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

  • that electric cells are characterized by their emf ε and internal resistance r as given by ε = I(R + r)
  •  that resistors can have variable resistance.

Standard level and higher level: There is no Standard level content
Additional higher level: 8 hours

IB DP Physics 2025 -Study Notes -All Topics

Cells – internal resistance

∙If we wish to consider the internal resistance of a cell, we can use the cell and the resistor symbols together, like this:
∙And we may enclose the whole cell in a box of some sort to show that it is one unit.
∙Suppose we connect our cell with its internal resistance r to an external circuit consisting of a single resistor of value R.
∙All of the chemical energy from the battery is being consumed by the internal resistance r and the external load represented by the resistance R.

 
• From \(E_p = qV\) we can deduce that the electrical energy being created by the cell is \(E_p = q\varepsilon\).

• The electrical energy being converted to heat energy by R is \(E_{p,R} = qV_R\).

• The electrical energy being converted to heat energy by r is \(E_{p,r} = qV_r\).

• From conservation of energy \(E_p = E_{p,R} + E_{p,r}\) so that \(q\varepsilon = qV_R + qV_r\).

Note that the current \(I\) is the same everywhere.

• From Ohm’s law \(V_R = IR\) and \(V_r = Ir\) so that \(\varepsilon = IR + Ir\).

Cells – terminal potential difference

EXAMPLE:

A cell has an unloaded voltage of 1.6 V and a loaded voltage of 1.5 V when a 330 Ω resistor is connected as shown.


What is the terminal potential difference t.b.d. of the cell?

▶️Answer/Explanation

SOLUTION:

 The terminal potential difference is the potential difference at the terminals of the cell where it connects to the external circuit.
∙This cell has an unloaded t.p.d of 1.6 V, and a loaded t.p.d. of 1.5 V. Note that the t.p.d. depends on the load.

Potential divider circuits

∙Consider a battery of ε = 6 V. Suppose we have a light bulb that can only use three volts. How do we obtain 3 V from a 6 V battery?
∙A potential divider is a circuit made of two (or more) series resistors that allows us to tap off any voltage we want that is less than the battery voltage.
∙The input voltage is the emf of the battery.
∙The output voltage is the voltage drop across R2.
∙Since the resistors are in series R = R1 + R2.

● From Ohm’s law the current I of the divider is given by
$ I = \frac{V_{IN}}{R} = \frac{V_{IN}}{R_1 + R_2} $

● But \( V_{OUT} = V_2 = I R_2 \), so that
$ V_{OUT} = I R_2$
$ = \left( \frac{V_{IN}}{R_1 + R_2} \right) (R_2). $

PRACTICE:
Find the output voltage if the battery has an emf of 9.0 V, $R_1$ is a 2200 Ω resistor, and $R_2$ is a 330 Ω resistor.

▶️Answer/Explanation

SOLUTION:
• Use \(V_{OUT} = V_{IN} \left( \frac{R_2}{R_1 + R_2} \right) = 9 \left( \frac{330}{2200 + 330} \right)\)
\(V_{OUT} = 9 \left( \frac{330}{2530} \right) = 1.2 \, \text{V}\).

FYI
• The bigger R₂ is in comparison to R₁, the closer \(V_{OUT}\) is in proportion to the total voltage.

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