Current Electricity

Cells, EMF and Internal Resisance


  • A cell is device which converts chemical energy into electrical energy.
  • The EMF of a cell is defined as the work done in moving unit positive charge in the whole circuit.
  • The EMF of a cell is depends only on nature of electrodes and electrolyte.
  • Internal resistance is the resistance offered by electrolyte between anode and cathode.
  • Internal resistance depends on area and size of plates and distance between the plates. Electrolyte of temperature.
  • The terminal potential difference is the work done in moving unit positive charge from anode to cathode.
  • The voltage dropped across the terminals of internal resistance is called lost volt.
  • Terminal potential difference V = E – ir.
  • EMF developed in the cell against the emf of the cell called Back EMF.

  • \tt i = \frac{E_{1} + E_{2}}{r_{1} + r_{2} + R}
  • Terminal potential difference across first cell V1 = E1 – ir1.
  • Terminal potential difference across second cell V2 = E2 – ir2.
  • When "n" cells of emf E and internal resistance "r" are connected in series. Then current \tt i = \frac{nE}{R+ nr}
  • When out of ‘n’ cells ‘m’ cells are connected wrongly effective emf = (n – 2m) E.
  • If two cells of different EMF are connected in parallel \tt E_{eq} = \frac{E_{1} r_{2} + E_{1}r_{2}}{r_{1} + r_{2}}
  • Current “i” when E1, E2 connected in parallel \tt i = - \frac{E_{1}r{2} + E_{2} r_{1}}{r_{1}r_{2} + R(r_{1} + r_{2})}
  • When ‘n’ cells each of emf ‘E’ and internal resistance ‘r’ are connected in parallel. Current \tt I = \frac{E}{R+ (\frac{r}{m})}
  • If R <<  \tt \frac{r}{m} Then \tt I = \frac{mE}{r}
  • If R >>  \tt \frac{r}{m} Then \tt I = \frac{E}{R}
  • "n" cells in series such ‘m’ cells are in parallel. Then Net resistance of circuit \tt R + \frac{nr}{m}.
  • Current in the above \tt i = \frac{nmE}{mR + nr}.

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1. Relation between ε, V and R
The voltage across R is
V = IR