Physics · Current Electricity · NEET
No. R is the external resistance (the bulb, wire, or resistor outside the cell). Internal resistance r sits INSIDE the cell. In a simple loop both carry the same current I, so the total resistance is (R + r), and current I = E / (R + r). Only R gives you useful output; r just wastes energy as heat inside the cell.
A cell drives current through the outside circuit, but the current must also travel back inside the cell through the electrolyte from the negative to the positive plate. That electrolyte (and the electrodes) is not a perfect conductor, so it offers a small resistance r. NCERT calls this the internal resistance of the cell. Old dry cells have high r; fresh electrolytic cells have low r.
For NEET numericals treat r as a fixed property of the cell, given in ohms. In real life r rises as a cell drains or gets old, but every NEET problem gives you a constant value of r. So use it as a normal series resistor.
The ohm, symbol capital omega, exactly like any other resistance. It is a resistance, so its unit is never volts or amperes.
In series. The real cell = ideal emf source E in series with the small resistor r. That is why the same current I flows through both, and why the internal drop is I times r, giving terminal voltage V = E - Ir.
Use V = E - Ir with I = V/R (current through the external resistor R). Substitute to get r = R(E - V)/V, i.e. r = R(E/V - 1). Just plug in emf E, terminal voltage V and external resistance R.
The terminal voltage of a battery of emf 10 V and internal resistance 1 ohm, connected to an external resistance of 4 ohm, is:
A resistor is connected to a battery of emf 12 V and internal resistance 2 ohm. If the current is 0.6 A, the terminal voltage of the battery is:
The emf of a cell (internal resistance 1 ohm) balances at 330 cm on a potentiometer. With a 2 ohm external resistance across the cell, the balance length is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
r = R(E - V)/V, which is the same as r = R(E/V - 1), where E is the emf, V is the terminal voltage and R is the external resistance. It comes from combining V = E - Ir with I = V/R.
When the cell supplies current I to an external circuit, V = E - Ir. The terminal voltage V is the emf E minus the internal voltage drop Ir. When the cell is being charged, the sign flips: V = E + Ir.
Only when no current flows (open circuit, I = 0) or when the internal resistance r is zero (an ideal cell). In both cases the Ir term vanishes, so V = E.
It hurts. Higher r means a bigger internal drop Ir, so less voltage and power reach the external circuit. Fresh cells keep r low; old or dry cells have high r, which is why torch light dims as batteries age.
When R = 0, the current is limited only by r: I(max) = E/r. This maximum short-circuit current is set entirely by the internal resistance, which is why a small r can give a dangerously large current.
