Question

3 identical resistors R1, R2, R3 are connected in Parallel, find the equivalent resistance in both the cases with a circuit diagram.

Answer 1

Answer:

Since, in series combination the values of resistances are added, the value of equivalent resistance is larger than the largest value of resistance in the combination of resistors.

In parallel:

In parallel connection, the value of equivalent resistance is smaller than the smallest value of resistance in the combination of resistors.

Answer 2

$\mathtt{\bf{\large{\underline {\red{ANSWER : - }}}}}$

GIVEN :-

✪ Resistors

• R1
• R2
• R3

✪ Circuit

• In parallel

✪ Current, I

• I1
• I2
• I3

✪ Voltage

• V

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TO FIND :-

• Equivalent resistance

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SOLUTION :-

According to the Ohm's law :

$V = IR \\ \\ I = \frac{V}{R} \\ \\ = > I1 = \frac{V}{R1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = > I2 = \frac{V}{R2} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = > I3 = \frac{V}{R3} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ So, \: I = I1 + I2 + I3 \\ \\ \frac{V}{R} = \frac{V}{R1} + \frac{V}{R2} + \frac{V}{R3}$

By taking V as common,

$\frac{V}{R} = \: V \: ( \: \frac{1}{R1} +\frac{1}{R2} +\frac{1}{R3} \: )$

Now, V from both the sides got cancelled.

So, equivalent resistance is :

$\mathtt{\bf{\large{\ {\red{ \frac{1}{R} = \frac{1}{R1} +\frac{1}{R2} +\frac{1}{R3}}}}}}$

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