AB and CD are two uniform resistance wires of lengths $$100$$ cm and $$80$$ cm, respectively. The connections are shown in the figure. The cell of emf $$5$$ V is ideal while the other cell of emf E has internal resistance $$2$$ Ω A length of $$20$$ cm of wire CD is balanced by $$40$$ cm of wire AB. Find the emf E in volt, if the reading of the ideal ammeter is $$2$$ A. The other connecting wires have negligible resistance.

Question

AB and CD are two uniform resistance wires of lengths $$100$$ cm and $$80$$ cm, respectively. The connections are shown in the figure. The cell of emf $$5$$ V is ideal while the other cell of emf E has internal resistance $$2$$  Ω A length of $$20$$ cm of wire CD is balanced by $$40$$ cm of wire AB. Find the emf E in volt, if the reading of the ideal ammeter is $$2$$ A. The other connecting wires have negligible resistance.

Infinity Learn · Accepted Answer

Potential difference across wire AB $$=$$ $$5$$ VPotential difference across $$40$$ cm of this wire $$5100$$  × $$40=2$$ V.So potential difference across $$20$$ cm of wire CD $$=$$ $$2V$$.∴  Potential difference across wire CD $$=$$  $$220$$  ×  $$80=8$$ VPotential difference across $$2$$  Ω resistor $$=$$ $$2$$ x $$2$$ $$=$$ $$4$$ V∴ Emf of the cell $$=$$  $$8$$ $$+$$ $$4$$ $$=$$ $$12$$ V

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