Question

Two resistances R1 and R2 are connected in parallel. Total current flowing through the circuit is I. Derive expressions for currents flowing through two resistances.​

Answer 1

Answer:

Explanation: i hv send the attachment hope it helps

Answer 2

$I_2=\frac{V.R_1}{R_1.R_2}$

&

$I_1=\frac{V.R_2}{R_1.R_2}$ are the respective currents.

Explanation:

When 2 resistances are in parallel.

Then we have an equivalent resistance as:

$\frac{1}{R_e} =\frac{1}{R_1} +\frac{1}{R_2}$

$\frac{1}{R_e} =\frac{R_1+R_2}{R_1.R_2}$

$R_e=\frac{R_1.R_2}{R_1+R_2}$

From Ohm's law we have the total current in the circuit as:

$I=\frac{V}{R_e}$

$I=\frac{V}{(\frac{R_1.R_2}{R_1+R_2} )}$

$I=\frac{V(R_1+R_2)}{R_1.R_2}$

Now the current in the resistance 1:

$I_1=\frac{V}{R_1}$

Now the current in resistor 2:

$I_2=I-I_1=\frac{V(R_1+R_2)}{R_1.R_2} -\frac{V}{R_1}$

$I_2=\frac{V.R_1}{R_1.R_2}$

&

$I_1=\frac{V.R_2}{R_1.R_2}$