Question

Find equivalent resistance of the given circuit and current through each resistor.

Answer 1

Given:-

• 3 Resistance are connected in parallel

To Find :-

• We have to find the equivalent resistance of the given Circuit and the Current through each resistor .

• They are connected in parallel ,So by using formula to find the resistance in Parallel combination -

Solution:-

$\underline{\boxed{\purple{ \sf\ \ \dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+. \ .\ .\ .\ \dfrac{1}{R_n}}}}$

$\sf{We\ have\ }\begin{cases}\sf{R_1=10k\Omega}\\\sf{R_2=2k\Omega}\\\sf{R_3=1k\Omega}\end{cases}$

$\dashrightarrow\sf\ \dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}\\ \\ \\ \dashrightarrow\sf\ \dfrac{1}{R_p}=\dfrac{1}{10}+\dfrac{1}{2}+\dfrac{1}{1}\\ \\ \\ \dashrightarrow\sf\ \dfrac{1}{R_p}=\dfrac{1+5+10}{10}\\ \\ \\ \dashrightarrow\sf\ \dfrac{1}{R_p}=\dfrac{16}{10}\\ \\ \\ \dashrightarrow\sf\ R_p= \cancel{\dfrac{10}{16}}\\ \\ \\ \dashrightarrow\sf\ R_p=\dfrac{5}{8} \longmapsto (0.625k\Omega)\\ \\ \sf\ 1\ kilo\Omega= 1000\Omega\\ \\ \\ \dashrightarrow\ \sf or\ \underline{\boxed{\sf\ R_p=625\Omega}}$

___________________________

• Now Current
• Voltage=9V
• we know that Current is inversely proportional to Resistance If resistance increases current decreases
• we know that in parallel combination Voltage remains Constant
• Using ohm's Law

$\sf \Big\lgroup\ V= IR\Big\rgroup\\ \\ \\ \dashrightarrow\sf\ I_1=\dfrac{V}{R_1}\\ \\ \sf\ \ V=9V\ \ and\ R_1=\ 10k\Omega= 10000\Omega\\ \\ \\ \dashrightarrow\sf\ I_1=\dfrac{9}{10000}\\ \\ \\ \dashrightarrow\underline{\boxed{\sf Current_1= 0.0009A}}\\ \\ \dashrightarrow\sf\ I_2=\dfrac{V}{R_2}\\ \\ \sf\ \ V=9V\ \ and\ R_2=\ 2k\Omega= 2000\Omega\\ \\ \\ \dashrightarrow\sf\ I_1=\dfrac{9}{2000}\\ \\ \\ \dashrightarrow\underline{\boxed{\sf Current_2= 0.0045A}}\\ \\ \\ \dashrightarrow\sf\ I_3=\dfrac{V}{R_3}\\ \\ \sf\ \ V=9V\ \ and\ R_3=\ 1k\Omega= 1000\Omega\\ \\ \\ \dashrightarrow\sf\ I_1=\dfrac{9}{1000}\\ \\ \\ \dashrightarrow\underline{\boxed{\sf Current_3= 0.009A}}$

Answer 2

Explanation:

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