Question

two resistances R1 and R2 are connected in parallel total current flowing through circuit is I derive expressions for current flowing through two resistances​

Answer 1

Explanation:

If R1 is removed then the total current going through the circuit has decreased (since you've increased resistance), but the current going through R2 remains the same. The same logic applies if you remove R2 instead of R1. If you remove them both, then no current runs through either.

Answer 2

Expressions for current flowing through two resistances in parallel are given below.

Explanation:

As, it is given that the two resistances are in parallel and we know current in parallel is different for different resistors. As, we know voltage in parallel connection is same for both the resistors.

So,  the expression for resistances are,

                           ⇒   V = $I_{1} R_{1}$

    This is the expression for resistor 1.

                            ⇒  $R_{1}$ = resistor 1.

                             ⇒ $I_{1}$ = current in resistor one.

                             

                                    ⇒   V = $I_{2} R_{2}$

            This is the expression for resistor 2.

                                        ⇒  $R_{2}$ = resistor 2.

                             ⇒ $I_{2}$ = current in resistor two.