Define internal resistance of a cell

\( \newcommand\) If we take the point A as having zero potential, we see that the potential of the point B will be E - \(Ir\), and this, then, is the potential difference across the poles of the cell when a current \(I\) is being taken from it.

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Internal Resistance Formula Internal resistance refers to the opposition to the flow of current offered by the cells and batteries themselves resulting in the generation of heat. Internal resistance is measured in Ohms. The relationship between internal resistance (r) and emf (e) of cell s given by. e = I (r + R) Where, e = EMF i.e. electromotive force (Volts), I = current (A), R = Load resistance, and r is the internal resistance of cell measured in ohms. On rearranging the above equation we get; e = IR + Ir or, e = V + Ir In the above equation, V is the potential difference (terminal) across the cell when the current (I) is flowing through the circuit. Note: The emf (e) of a cell is always greater than the potential difference (terminal) across the cell Example: 1 The potential difference across the cell when no current flows through the circuit is 3 V. When the current I = 0.37 Ampere is flowing, the terminal potential difference falls to 2.8 Volts. Determine the internal resistance (r) of the cell? Solution: e = V + Ir Or, e – V = Ir Or, (e – V)/I = r Therefore, r = (3.0 – 2.8)/0.37 = 0.54 Ohm. Due to the Internal Resistance of the cell, the electrons moving through the cell turns some of the electrical energy to heat energy. Therefore, the potential difference available to the rest of the circuit is: V = E (EMF of cell) – Ir (the p.d. across the internal resistor)

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Resistance is a physical quantity that is the measurement of the ability to resist the flow of electrons or current. The internal resistance of a cell or battery is the resistance offered by it. This occurs due to the presence of ions which obstruct the flow of electrons. It has some specific properties which distinguish it from normal resistance. Unlike the resistance of a conductor, it neither increases with temperature nor has a definite specific resistance. In the following segment, we are going to discuss the pros and cons of it. Definition The internal resistance of a cell is the ability to resist or restrict the flow of current or electrons. It’s exactly the reciprocal of the conductivity of the cell. An ideal cell will have zero resistance while a normal lithium-ion battery has internal resistance typically between 155m Ohm to 778m Ohm. Origin The conductivity of any charge carrier is the sum of the product of mobility and electric field and the reciprocal of it gives us the resistance. In a cell, two major charge carriers are electrons and ions. The reciprocal of their total conductivity gives internal resistance. Without those ions it’s impossible to build a battery hence the construction of a battery without internal resistance is impossible. Factors affecting internal resistance The internal resistance a cell-dependent on the following factors – • It decreases as the mobility of the ions in the battery increases. • It depends on the type and concentration of th...

As shown in the video, to find the EMF and internal resistance of a cell, the following circuit is set up. The variable resistor is altered and readings of potential differences across the terminals of the cell and current through the cell are taken. A graph of these results is then drawn as shown below. At the point at which the line meets the terminal potential difference axis there is no current drawn from the cell. This is called the open circuit potential of the circuit. Because there is no current there will be no lost volts so this value is the EMF of the cell. So the point where the line meets the terminal potential difference axis, (the y-axis intercept) is the EMF of the cell. At the point where the line meets the current axis, (the x-axis intercept) the maximum current is drawn from the cell. This happens when the load resistance, \(R= 0\Omega.\) This would be achieved by short circuiting the cell (this should be avoided as the cell could overheat and it is potentially dangerous). The maximum current is called the short circuit current , \(I_\) .

The potential difference between the electrodes of the cell when current is drawn from it is called the terminal voltage of the cell. It is smaller than the e.m.f. of the cell because of the internal resistance of the cell. When current flows, some energy is spent in overcoming the internal resistance (r) of the cell. V = e m f − I r Factors affecting internal resistance The internal resistance of a cell depends on: • Surface area of electrodes (more surface area → less resistance) • Distance between the electrodes (more distance → more resistance) • Nature and concentration of electrolyte (higher concentration → more resistance) • Temperature of electrolyte (more temperature → more resistance) A cell of emf 'E' and internal resistance 'r' is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current i. It is found that when R = 4 Ω, the current is 1 A when R is increased to 9 Ω, the current reduces to 0 . 5 A. Find the values of the emf E and internal resistance r