Question

derive an expression for the equivalent resistance R1 R2 and R3 are connected in parallel ​

Answer 1

Answer:

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Answer 2

$\huge{\underline{\bf{\red{Answer:-}}}}$

we know that,

If resistors are connected in parallel then the potential difference is same and current passed to each resistor is different.

• V = potential difference
• I = current
• R = resistance

According to ohm's Law:-

$\bf\: \pink{V = IR} \\ \\ \longmapsto \rm \: \pink{I = \frac{V}{R_ p} } \\ \\ \longmapsto \rm \:I_1=\frac{V}{R_1} .......(i)$

$\longmapsto \rm\:I_2=\frac{V}{R_2}\:..........(ii)\\ \\ \longmapsto \rm\:I_3=\frac{V}{R_3}\: .........(iii)$

From eq. (i) ,(ii) , and (iii)

we get,

$\longmapsto \rm\:I_p=I_1+I_2+I_3\:$

$\longmapsto \rm\:I_p=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3}\:$

$\longmapsto \rm\:\frac{V}{R_p}=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_2}\:$

$\longmapsto \rm\:V(\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3})\:$

So,

expression for the equivalent resistance R1 R2 and R3 are connected in parallel is :-

$\longmapsto \bf\:V(\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3})\:$

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