Current Electricity - Internal Resistance of a Cell
current electricity internal resistance of a cell is explained with EMF, terminal voltage, internal resistance, cell combinations, maximum power transfer theorem, V-I graphs, SVG diagrams and exam-level practice for CBSE, NEET, JEE Main, JEE Advanced, IB, AP, IGCSE and ICSE Physics.
If Internal Resistance, Terminal Voltage, EMF, Maximum Power Transfer Theorem or Cell Combination concepts are not clear, students may contact Kumar Sir for one-to-one Physics guidance.
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1. Complete Formula Sheet
EEMF of cell, unit volt.VTerminal voltage, unit volt.rInternal resistance, unit ohm.RExternal resistance, unit ohm.I = E/(R+r)Current in complete circuit.V = E - IrTerminal voltage during discharge.V = IRVoltage across external resistance.r = (E - V)/IExperimental internal resistance.P = I²RPower delivered to load.Ploss = I²rPower lost inside cell.η = R/(R+r)Efficiency of cell.R = rMaximum power transfer condition.Pmax = E²/(4r)Maximum load power.[E]=[V]=ML²T⁻³A⁻¹Dimensional formula of voltage.[R]=[r]=ML²T⁻³A⁻²Dimensional formula of resistance.2. What Is Internal Resistance?
Internal resistance is the opposition offered inside a cell due to electrolyte, electrodes and ionic motion. Because of it, terminal voltage becomes less than EMF when current is drawn.
Why it exists: ions move through electrolyte and face opposition, so every real cell has internal resistance.
Ideal cell: would have r = 0, but practical cells always have some internal resistance.
EMF vs terminal voltage: EMF is open-circuit potential; terminal voltage is actual output under load.
Real-life example: an old battery shows voltage drop when connected to a high-current device.
Temperature: internal resistance usually changes with temperature and electrolyte condition.
Loading: heavy load means large current, so internal voltage drop Ir becomes large.
3. Types of Cells and Internal Resistance
| Cell | Approximate Internal Resistance | Reason |
|---|---|---|
| Leclanche cell | Relatively high | Higher electrolyte/electrode limitations. |
| Daniell cell | Moderate | Liquid electrolyte gives better ionic path. |
| Dry cell | Moderate to high | Paste electrolyte and ageing effects. |
| Lead acid cell | Low | Large plates and strong electrolyte. |
| Alkaline cell | Lower than ordinary dry cell | Better chemical design. |
| Lithium cell | Low | High energy density and optimized electrodes. |
| Button cell | Often high for large current | Small size limits current delivery. |
| Rechargeable cells | Usually low | Designed for repeated current delivery. |
4. Beautiful SVG Diagrams
5. Derivations
Terminal Voltage: V = E - Ir
1
Inside the cell, current I passes through internal resistance r.
2
Internal voltage drop is Ir.
3
Terminal voltage is EMF minus internal drop: V = E - Ir.
Current: I = E/(R+r)
1
Total circuit resistance is external plus internal: R + r.
2
Using Ohm's law for complete circuit: E = I(R+r).
3
Therefore I = E/(R+r).
Internal Resistance: r = (E - V)/I
1
Start with V = E - Ir.
2
Rearrange: Ir = E - V.
3
Divide by I: r = (E - V)/I.
Maximum Power Transfer Theorem
1
Load power is P = I²R.
2
Substitute I = E/(R+r): P = E²R/(R+r)².
3
Differentiate with respect to R: dP/dR = E²[(R+r)² - 2R(R+r)]/(R+r)4.
4
For maximum power, numerator is zero: (R+r) - 2R = 0.
5
So R = r.
6
Put R = r in P = E²R/(R+r)² to get Pmax = E²/(4r).
6. V-I Graph
Experimentally, plot terminal voltage V against current I. The straight line follows V = E - Ir. Its y-intercept gives EMF E and magnitude of slope gives internal resistance r.
7. Conceptual Questions
What if r increases? Current decreases, terminal voltage drops more and power loss inside cell increases.
Why terminal voltage decreases on loading? Because a current is drawn and internal drop Ir appears.
Why EMF remains almost constant? EMF depends on chemical nature of cell, not directly on load current.
Why old cells have higher r? Chemical changes, electrolyte degradation and electrode effects increase opposition to ionic motion.
Effect of electrode separation: larger separation usually increases ionic path and internal resistance.
Rechargeable cells: often designed with lower internal resistance for higher current delivery.
8-12. Exam Question Bank With Accordion Solutions
Click any question to open the answer and explanation.
13. Common Errors
14. Quick Revision Sheet
Terminal voltage: V = E - Ir.
Complete circuit current: I = E/(R+r).
Internal resistance: r = (E - V)/I.
Load power: P = E²R/(R+r)².
Maximum power: R = r and Pmax = E²/(4r).
V-I graph: intercept = E, slope = -r.
Still confused about Internal Resistance, EMF, Terminal Voltage or Maximum Power Transfer Theorem?
Contact Kumar Sir for one-to-one Physics Classes.
Phone: +91-9958461445
Website: https://kumarphysicsclasses.com