Physics, asked by pihutandon2004, 5 hours ago

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

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Answers

Answered by MяMαgıcıαη
61

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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