Question

Two resistances R1 and R 2 are connected with a cell in parallel. Find the ratio of current flowing through R1 to the current flowing through R2.

Answer 1

Answer:

The ratio of current in both of the given resistors is $\frac{I_{1}}{I_{2}} = \frac{R_{2} }{R_{1} }$

Explanation:

Here we have been given that two resistors which are $R_{1}$ and $R_{2}$ respectively are connected in parallel with a cell. We have been asked to find the current that is flowing through the resistor $R_{1}$ to the current flowing through $R_{2}$

The current in both the resistors will be different as we know that in parallel connection of the given resistors the current through each of them is different, but the voltage remains the same.

From ohm's law, we have,

V = IR

Where V is the potential difference between the respective ends of the resistors, I is the amount of current flowing in the circuit and the R is the resistance.

Then we have,

Current ($I_{1}$) in the $R_{1}$ resistor is as follows:

$I_{1} = \frac{V}{R_{1} }$

Current ($I_{2}$) in the $R_{2}$ resistor is as follows;

$I_{2} = \frac{V}{R_{2} }$

The ratio of the currents in both the resistors is as follows;

$\frac{I_{1}}{I_{2}} =\frac{\frac{V}{R_{1} }}{\frac{V}{R_{2} }}$

⇒ $\frac{I_{1}}{I_{2}} = \frac{R_{2} }{R_{1} }$

Therefore the ratio of current in both the resistors is $\frac{I_{1}}{I_{2}} = \frac{R_{2} }{R_{1} }$