Cells, EMF, Internal Resistance — Revision Notes

⚡ 30-Second Revision

EMF ($E$): — Max potential difference (open circuit).
Internal Resistance ($r$): — Resistance within cell.
Terminal Voltage ($V$): — Actual voltage across terminals (closed circuit).
Discharging Cell: — $V = E - Ir$
Charging Cell: — $V = E + Ir$
Current: — $I = \frac{E}{R+r}$
Power to External Load: — $P_{ext} = I^2R = VI$
Power Lost Internally: — $P_{int} = I^2r$
Cells in Series (Aiding): — $E_{eq} = nE$, $r_{eq} = nr$
Cells in Parallel (Identical): — $E_{eq} = E$, $r_{eq} = r/n$
Cells in Parallel (Non-identical): — $E_{eq} = \frac{E_1/r_1 + E_2/r_2}{1/r_1 + 1/r_2}$, $rac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2}$

2-Minute Revision

Cells are devices converting chemical energy to electrical energy, characterized by their Electromotive Force (EMF, $E$) and internal resistance ($r$). EMF is the maximum potential difference when no current is drawn.

Internal resistance is the opposition to current flow within the cell itself, causing a voltage drop ($Ir$) when current ($I$) flows. The terminal potential difference ($V$) is the actual voltage available at the terminals, given by $V = E - Ir$ during discharge.

If the cell is being charged, $V = E + Ir$. The total current in a simple circuit with external resistance $R$ is $I = \frac{E}{R+r}$. Power delivered to the external circuit is $I^2R$, while $I^2r$ is dissipated internally.

When cells are connected in series, their EMFs and internal resistances add up ($E_{eq} = nE$, $r_{eq} = nr$). For identical cells in parallel, the EMF remains the same ($E_{eq} = E$), but the equivalent internal resistance decreases ($r_{eq} = r/n$), enhancing current capacity.

Remember that EMF is an intrinsic property, while terminal voltage is load-dependent.

5-Minute Revision

Let's consolidate the crucial aspects of cells, EMF, and internal resistance for NEET. A cell is essentially a chemical energy converter. Its inherent 'push' is the Electromotive Force ($E$), measured in Volts, which is the maximum potential difference it can establish across its terminals when no current is flowing (open circuit).

However, no cell is ideal; it possesses an internal resistance ($r$), arising from the electrolyte and electrodes. This internal resistance causes a voltage drop ($Ir$) when a current ($I$) is drawn from the cell.

Consequently, the actual voltage available to the external circuit, known as the terminal potential difference ($V$), is less than the EMF, following the relation $V = E - Ir$. If the cell is being charged, current flows into it, and the terminal voltage becomes $V = E + Ir$.

For a simple circuit with an external resistance $R$, the total current is $I = \frac{E}{R+r}$. The power delivered to the external load is $P_{ext} = I^2R$, while power lost as heat within the cell is $P_{int} = I^2r$. The total power generated by the cell is $EI$. Maximum power transfer occurs when $R=r$.

Combinations of cells are also vital. For $n$ identical cells in series, the equivalent EMF is $E_{eq} = nE$, and the equivalent internal resistance is $r_{eq} = nr$. This setup increases the total voltage.

For $n$ identical cells in parallel, the equivalent EMF remains $E_{eq} = E$, but the equivalent internal resistance decreases to $r_{eq} = r/n$, which is beneficial for delivering higher currents or extending battery life.

For non-identical cells in parallel, specific formulas are used: $E_{eq} = \frac{sum (E_i/r_i)}{sum (1/r_i)}$ and $rac{1}{r_{eq}} = sum \frac{1}{r_i}$. Always distinguish between EMF (source property) and terminal voltage (load-dependent voltage) and practice numerical problems involving all these scenarios.

Prelims Revision Notes

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Cell Basics: — Converts chemical to electrical energy.
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**EMF ($E$):**

* Maximum potential difference across terminals. * Measured when no current is drawn (open circuit, $I=0$). * Unit: Volt (V). * Intrinsic property of the cell.

1
**Internal Resistance ($r$):**

* Resistance offered by electrolyte and electrodes within the cell. * Causes voltage drop $Ir$. * Factors affecting $r$: nature of electrolyte/electrodes, distance between electrodes, immersed area, temperature, age.

1
**Terminal Potential Difference ($V$):**

* Actual potential difference across terminals when current flows. * Discharging cell: $V = E - Ir$. Here, $V < E$. * Charging cell: $V = E + Ir$. Here, $V > E$. * Open circuit: $V = E$ (since $I=0$). * Short circuit: $R=0$, $V=0$, $I_{max} = E/r$.

1
Current in Circuit: — $I = \frac{E}{R+r}$, where $R$ is external resistance.
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Power:

* Total power generated by cell: $P_{total} = EI$. * Power delivered to external load: $P_{ext} = VI = I^2R = V^2/R$. * Power dissipated internally: $P_{int} = I^2r$. * Conservation of energy: $EI = I^2R + I^2r$. * Maximum power transfer: $P_{ext}$ is max when $R=r$.

1
Cells in Series:

* $n$ identical cells ($E, r$) in series (aiding): $E_{eq} = nE$, $r_{eq} = nr$. * Current: $I = \frac{nE}{R+nr}$. * If cells oppose, subtract EMFs, but internal resistances still add.

1
Cells in Parallel:

* $n$ identical cells ($E, r$) in parallel: $E_{eq} = E$, $r_{eq} = r/n$. * Current: $I = \frac{E}{R+r/n}$. * Non-identical cells ($E_1, r_1, E_2, r_2$): $E_{eq} = \frac{E_1/r_1 + E_2/r_2}{1/r_1 + 1/r_2}$, $rac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2}$.

1
Key Distinction: — EMF is a source characteristic; Terminal Voltage is a circuit characteristic dependent on load.

Vyyuha Quick Recall

EMF is 'E' for 'Everything' (total potential). Internal resistance 'r' 'reduces' it. Terminal voltage 'V' is 'Visible' (what you measure). So, 'E' minus 'Ir' equals 'V' (E - Ir = V). For series, 'N' times 'E' and 'N' times 'r'. For parallel, 'E' stays 'E', but 'r' gets 'Reduced' (r/N).