Question

A battery of e.m.f. 3 volt and internal resistance 1.0 ohm is connected in series with copper voltameter. The current flowing in the circuit is 1.5 amperes. The resistance of the voltameter will be:
A. Zero
B. 1.0 ohm
C. 1.5 ohm
D. 2.0 ohm

Answer 1

Hint:Apply the concept of Ohm’s law which states the relationship between current and potential differences. Most conductors' current is directly proportional to the voltage applied across it. By this, we can find the relationship between e.m.f and internal resistance.






Formula used:
$e=i\lgroup~r+R\rgroup$
Where e = electromotive force in Volts, I = current in Amperes, R = load resistance, and r is the cell's internal resistance in ohms.




Complete answer:
Internal resistance is the resistance to the flow of current provided by the cells and batteries themselves, which results in the generation of heat. Ohms are used to measure internal resistance. The relationship between internal resistance (r) and electromotive force (e) of cells is given by,
$e=i\lgroup~r+R\rgroup$
Given: $i=1.5A$
$e=3volt$
$R_{net}=1+R$
We know,
$e=i\lgroup~r+R\rgroup$
On rearranging the above equation we get,
$i=\dfrac{e}{r+R}$
Substituting the values we get,
$i=\dfrac{3}{1+R}$
$\Rightarrow\dfrac{3}{2}=\dfrac{3}{1+R}$ (Since we can write 1.5 in terms of fraction for simplicity)
$\Rightarrow~R=1~ohm$
Therefore, the resistance of the voltameter will be 1 ohm.
Thus, the correct option is B.






Note: The resistance of the voltmeter is equivalent to the load resistance as specified in the formula. Load resistance is also resistance, but it has a very precise meaning in the context of electric circuits; it is the resistance connected between a circuit's output stage and the ground. The power supplied by the circuit is drawn in by this resistance. This resistance also represents the resistance of the device or circuit to which the output stage is connected.