Question

Q3. FIND TOTAL RESISTANCE AND TOTAL CURRENT IN THE CIRCUIT GIVEN BELOW:
IF THE BATTERY OF 6 V IS CONNECTED BETWEEN POINTS A AND B
WW
222
w
A
B
w
292

Answer 1

Answer :-

$\quad\pink{\bigstar}$ Equivalent resistance $\leadsto\:{\boxed{\tt{\blue{3\:\Omega}}}}$

$\quad\pink{\bigstar}$ Total current $\leadsto\:{\boxed{\tt{\blue{2\:A}}}}$

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• Given :-

• $\sf {R_{1} = \bf{1\:\Omega}}$

• $\sf {R_{2} = \bf{1\:\Omega }}$

• $\sf{ R_{3} = \bf{2\:\Omega}}$

• $\sf {R_{4} =\bf{ 2\:\Omega}}$

Where,

• $\sf {R_{1}\:and \:R_{2} \:are\: in \:\bf{parallel}}$

• $\sf {R_{3}\:and \:R_{4} \:are\: in \:\bf{series}}$

• To Find :-

• Equivalent Resistance = ?

• Total Current = ?

• Solution :-

⌬ Finding "Equivalent resistance" :-

• We clearly know that for resistors $\sf R_{1}$ and $\sf R_{2}$, 'resistance in series' is given by :-

$\qquad\pink{\bigstar}\:{\underline{\boxed{\bf{\green{RS = R_{1} + R_{2}}}}}}$

⌬ Putting all known values :-

➪ RS = 1 + 1

$\bigstar\:\underline{\underline{\bf{\red{RS = 2\:\Omega}}}}$

Also,

• For resistors $\sf R_{3}$ and $\sf R_{4}$, 'resistance in parallel' is given by :-

$\qquad\pink{\bigstar}\:{\underline{\boxed{\bf{\green{\dfrac{1}{RP} = \dfrac{1}{R_{3}} + \dfrac{1}{R_{4}}}}}}}$

⌬ Putting all known values :-

➪ $\sf \dfrac{1}{RP} = \dfrac{1}{2} + \dfrac{1}{2}$

➪ $\sf \dfrac{1}{RP} = \dfrac{1 + 1}{2}$

➪ $\sf \dfrac{1}{RP} = \dfrac{2}{2}$

➪ $\sf \dfrac{1}{RP} = {\cancel{\dfrac{2}{2}}}$

$\bigstar\:\underline{\underline{\bf{\red{RP = 1\:\Omega}}}}$

Therefore,

➪ Equivalent resistance = RS + RP

➪ Equivalent resistance = 2 + 1

$\bigstar\:\underline{\underline{\bf{\red{Equivalent\:resistance = 3\:\Omega}}}}$

Now,

⌬ Finding "Total current" :-

• We clearly know that, the 'current' is given by :-

$\qquad\pink{\bigstar}\:{\underline{\boxed{\bf{\green{Current = \dfrac{Voltage}{Resistance}}}}}}$

We have,

• Voltage = 6 V
• Resistance = 3 Ω

⌬ Putting all known values :-

➪ $\sf Current = \dfrac{6}{3}$

➪ $\sf Current = {\cancel{\dfrac{6}{3}}}$

$\bigstar\:\underline{\underline{\bf{\red{Total\:current = 2\:A}}}}$

Hence,

• Equivalent resistance = 3 Ω

• Total current = 2 A

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