Question

Two resistance are connected parallel and a current is sent through the combination. Then divides itself:
A. In the inverse ratio of resistance
B. In the direct ratio of resistance
C. Equally in both the resistance
D. In none of the above matter

Answer 1

Hint: Using the concept of parallel resistance. When resistance is connected parallelly then the current is divided. The distribution of current depends on the resistor connected to that branch. From the ohms current always follows least resistance.

Complete step by step answer:
As per the problem, two resistance are connected parallel and a current is sent through the combination. When this combined current is sent through the resistor then it gets divided according to the resistance present in that branch .From this statement we conclude that from our given option, option (C) is an impossible case as the resistance is connected parallel.

Now, we also know that according to Ohm's law the current always flows with the least resistance.
Hence with the help of ohm’s law we can write,
$V = IR$
Rearranging the above formula we will get current resistance relation,
$I = \dfrac{V}{R}$
Hence we get an inverse relationship between the current and the resistance.
We already get our current option that is (A).
Now we have to prove this for two resistance connected parallel to each other,

For first resistance:
${I_1} = \dfrac{V}{{{R_1}}} \ldots \ldots \left( 1 \right)$
For second resistance:
${I_2} = \dfrac{V}{{{R_2}}} \ldots \ldots \left( 2 \right)$
Here Voltage across the two resistance will remain constant as both of them are connected parallelly to each other.
Taking the ratio of equation $\left( 1 \right)$ to equation $\left( 2 \right)$ , we get
${I_1}:{I_2} = \dfrac{V}{{{R_1}}}:\dfrac{V}{{{R_2}}}$
Simplifying the constant term we will get,
${I_1}:{I_2} = \dfrac{1}{{{R_1}}}:\dfrac{1}{{{R_2}}}$
Now we can write the above equation as,
$\dfrac{{{I_1}}}{{{I_2}}} = \dfrac{{{R_2}}}{{{R_1}}}$
Hence two resistance are connected parallel and a current is sent through the combination.Then divides itself in the inverse ratio of resistance.

Hence, the correct answer is option A.

Note: Always keep in mind that the voltage always remains constant whenever any number of resistance are connected parallelly to each other. In short we can conclude from this above statement that currents and resistance are inversely related to each other whenever the resistances are connected parallel to each other.