Question

Two resistors 1k ohm and 2k ohm are connected
in parallel combination.
i] Find equivalent resistance of parallel combination
ii] When this parallel combination is
connected to 9 V supply, by neglecting
internal resistance calculate current
through each resistor.​

Answer 1

1) 0.67k ohm

2)9 and 4.5 mA

Answer 2

Answer:

i) Equivalent resistance = $0.67\ k\Omega$

ii) Current through 1 kiloohm  = 9 mA

iii) Current through 2 kiloohm  = 4.5 mA

Explanation:

Given:

• a = resistance of the first resistor = $1\ k\Omega$

• b = resistance of the second resistor = $2\ k\Omega$
• V = voltage across the parallel combination of both the resistors = 9 V

Assume:

• R = equivalent resistance of the parallel combination
• i = current through the first resistor
• I = current through the second resistor

When two resistors are in parallel combination, the equivalent resistance is given by:

$\dfrac{1}{R}=\dfrac{1}{a}+\dfrac{1}{b}\\\Rightarrow \dfrac{1}{R} = \dfrac{ab}{a+b}\Rightarrow R = \dfrac{ab}{a+b}\\\Rightarrow R = \dfrac{1\times2}{1+2}\\\Rightarrow R = 0.67\ k\Omega$

Since voltage across each resistors in a parallel combination is the same and equal to the voltage supplied to the combination.

$\therefore V = ia\\\Rightarrow i = \dfrac{V}{a}\\\Rightarrow i = \dfrac{9\ V}{1\ k\Omega}\\\Rightarrow i =9\ mA$

Similarly,  

$\therefore V = Ib\\\Rightarrow I = \dfrac{V}{b}\\\Rightarrow I = \dfrac{9\ V}{2\ k\Omega}\\\Rightarrow I =4.5\ mA$