Question

Find the equivalent
equivalent resistance.​

Answer 1

$\bigstar{\pmb{\sf Question }}$

• Obtain the Equivalent resistance

$\bigstar{\pmb{\sf Concept\: and\: formula }}$

• first, we need to find the equivalent resistance of this circuit. which can be given by the following formulas:-

$\underline\pink{\boxed{\bf R_{eq} = R_{1}+R_{2}+R_{3}....R_{n} }}$

• the above formula is used when the resistors are connected in series i.e end to end

$\underline\pink{\boxed{\bf \dfrac{1}{R_{eq}} = \dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}....\dfrac{1}{R_{n} }}}$

• the above formula is used when the resistors are connected in parallel

$\bigstar{\pmb{\sf Solution }}$

• Resistors, 5 ohm, 10 ohm and 5 ohm are connected parallelly. Hence, by using the formula, we can calculate the resistance of that region:-

$:\implies\sf\dfrac{1}{R_{eq}}=\dfrac{1}{5} + \dfrac{1}{10} +\dfrac{1}{5}$

$:\implies\sf\dfrac{1}{R_{eq}} =\dfrac{2+1+2}{10}$

$:\implies\sf\dfrac{1}{R_{eq}} =\dfrac{\cancel{5}}{\cancel{10}} =\dfrac{1}{2}$

$\therefore\sf R_{eq}=2\:ohms$

• Now, this equivalent resistance is connected in series with  other 10 ohm resistor.
• By, using series formula we shall calculate the equivalent resistance of the entire circuit.

$:\implies\sf R_{eq} = 2+10 = 12 \:ohms$

hence, our required answer is 12 ohms.

And we are done :D