Question

A cell of negligible resistance and e.m.f. 2 volt is connected to a series combination of 2, 3 and 5 ohms. The potential difference across the 3 ohm resistance will be
A. 6 V
B. 3V
C. $\dfrac{2}{3}V$
D. 0.6 V

Answer 1

Hint: The effective resistance in series connections of the resistor will be. When resistors are connected in series, the current through each resistor will be same and potential difference is not same while in parallel connection, potential difference across each resistor will be same and current will be different.

Complete step by step answer:
In a series connection containing two resistors, the voltage across the two ends of the circuit is directly proportional to the effective resistance in the circuit, i.e. \[V \propto R\]
As there is a series combination of 2, 3 and 5 ohms in the circuit. So, the effective resistance is
\[R = 2 + 3 + 5 = 10\] ohms
As the 3 ohms resistor constitutes only the three-tenths of the total resistance, so the voltage across the 3 ohms resistor will be \[\dfrac{3}{{10}} \times 2 = 0.6\,V\]
Hence the potential difference across the 3 ohm resistor will be 0.6 V.
Hence, the correct option is (D).

Note:Resistors are said to be in series connection, if the same current is flowing through each resistor when the same potential difference is applied across the combination. The effective resistance of a series combination of resistors is always greater than the resistance of an individual resistor. In a series connection, the current is the same in every resistor. The current in the circuit is independent on the relative positions of different resistors in the connection. The potential difference across any resistor in the circuit is directly proportional to the resistance of that resistor.