Question

Three resistors are combined such that a constant potential difference is applied across every resistor . calculate equivalent resistance of combination .​

Answer 1

Answer :-

• let R1 , R2 and R3 are three resistors across a source of V volt (potential difference is same for each resistor)

• Let I1, I2 and I3 are the current in R1, R2 and R3 respectively

and we know by ohm's law that,

$\boxed{ \bold{I = \frac{ V}{R} }}$

then,

$\bold{: \implies \: I1 = \frac{ V}{R1} } \\ \\ \bold{: \implies \: I2 = \frac{ V}{R2} } \\ \\ \bold{: \implies \: I3 = \frac{ V}{R3}}$

Then, the total current is

$\bold{I = I1 + I2 + I3}$

or

$\bold{ I = \frac{ V}{R1} + \frac{ V}{R2} + \frac{ V}{R3}}$

If the equivalent resistance of the combination is Re

then,

$\bold{I = \frac{ V}{Re}}$

here, we get

$\bold{ \frac{ V}{Re} = \frac{ V}{R1} + \frac{ V}{R2} + \frac{ V}{R3}} \\ \\ \bold{: \implies \frac{ \cancel{V} }{Re} = \cancel{V} \bigg(\frac{ 1}{R1} + \frac{ 1}{R2} + \frac{ 1}{R3} \bigg)} \\ \\ : \implies \boxed{ \bold{ \frac{ 1}{Re} = \frac{ 1}{R1} + \frac{ 1}{R2} + \frac{ 1}{R3}} } \: \: \: \: \: \: \:$

So, the reciprocal of equivalent resistance us equal to the sum of the reciprocals of the individual resistances.

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we can say, these resistors are connected in parallel combination because, Two or more resistances are called in parallel if same potential act across each resistance.