Question

if tow resistors of 10ohm are connected in parallel then find the effective resistance ​

Answer 1

Given :

Two resisors of 10 Ω are connected in parallel.

To Find :

Equivalent resistance of the parallel connection.

Solution :

❖ The reciprocal of the combined resistance of a number of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. i.e.,

$\dag\:\underline{\boxed{\bf{\orange{\dfrac{1}{R_1}+\dfrac{1}{R_2}+...+\dfrac{1}{R_n}=\dfrac{1}{R}}}}}$

By substituting the given values;

$\sf:\implies\:\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$

$\sf:\implies\:\dfrac{1}{R}=\dfrac{1}{10}+\dfrac{1}{10}$

$\sf:\implies\:\dfrac{1}{R}=\dfrac{2}{10}$

$\sf:\implies\:R=\dfrac{10}{2}$

$:\implies\:\underline{\boxed{\bf{\gray{R=5\:\Omega}}}}$

Knowledge BoosteR :

• In series combination, current flow through each resistor is same but potential differences across the resistors may be different.
• In parallel combination, potential difference on each resistor is same but the current flow through resistors may be different.

Answer 2

☯︎ Given that,

• $\sf \: Two \: resistors \: of \: \bold{10ohm} \: are \: connected \: in \: parallel.$

$\:$

☯︎ We've to find,

• $\sf \: \bold{Equivalent \: resistance} \: of \: the \: parallel \: combination.$

__________________________

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☯︎ As we know that, If the combination is parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of each of the individual resistances.

$\bigstar\underline{\boxed{\bold\purple{ \frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} + ... + \frac{1}{Rn} }}}$

$\underline\bold{substituting \: the \: values \: - }$

$\sf:\implies \: \frac{1}{R} = \frac{1}{10} + \frac{1}{10} \\ \\ \sf:\implies \: \frac{1}{R} = \frac{1 + 1}{10} \\ \\ \sf:\implies \: \frac{1}{R} = \frac{2}{10} \\ \\ \sf:\implies \: \frac{1}{R} = \cancel \frac{2}{10} \\ \\ \sf:\implies \: \frac{1}{R} = \frac{1}{5} \\ \\ \sf:\implies \: R \: = \underline{\boxed{\sf\purple{5 ohm}}}\bigstar$

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$\:$

$\sf\therefore{\underline{Hence \: the \: equivalent \: resistance \: is \: \bold{5ohm.}}}$