​Two resistors. A (10 Ω) and B (20 Ω) , are connected in parallel. The combination is connected to a 6V battery. The currents in A and B are respectively ___________. ​

Correct option is C

The correct answer is (C) ​0.6A and 0.3 A​.

Resistance in parallel combination:

• Three resistors connected in parallel to a battery of voltage V are depicted in the figure below.
• In this type of connection, the resistors are typically connected on parallel wires that originate from a common point.
• The voltage that flows through each resistor is the same in this instance.
• The equivalent resistance of the three resistances is depicted in the figure on the right.
• The equation for the relationship between voltage and current is, $$V=IR$$​ It can be rewritten as, $$I=\frac{V}{R}$$​
• The voltages across individual resistors will be,$${I_1} = \frac{V}{R_1},{I_2} = \frac{V}{R_2}, {I_3} = \frac{V}{R_3}$$​The sum of the current flowing through each resistance will be, $$I= {I_1}+{I_2}+{I_3}$$​ By substituting individual voltages for the expressions, $$I = \frac{V}{R_1} + \frac{V}{R_2} +\frac{V}{R_3}$$​Let the equivalent capacitance be $$R, \frac{V}{R} = \frac{V}{R_1} +\frac{V}{R_2} + \frac{V}{R_3}$$​
• The relation becomes, when the above equation is simplified. $$\frac{1}{R}=\frac{1}{R_1}+ \frac{1}{R_2}+ \frac{1}{R_3}$$​

Calculations

Two resistors, A=10 Ω and B=20 Ω, are connected in parallel

Voltage= 6V

We know, $$V=IR, I=\frac{V}{R}$$​

$$I_1= \frac{6}{10}= \frac{3}{5}= 0.6A$$​

$$I_2= \frac{6}{20}= \frac{3}{10}= 0.3A$$​