Question

Derive an equation for equivalent of resiatance when two resistance connected in a series ​​

Answer 1

Answer:

Derive an expression for the equivalent resistance of three resistances connected in series. Series combination: If a number of resistors are joined together so that the current flowing across each resistor is the same, then the resistances are said to be connected in series.

Answer 2

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$\bold{ \underline{ \underline{ \bold{combination \: of \: resistances}}}}→$

1). Series combination ➜

→ When two or more resistances are connected in such a way that same current passes through each resistor then combination is called series combination

2). Parallel combination ➜

→ two or more resistances are called in parallel if same potential act across each resistance.

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ᴥ︎︎︎ derivation of equivalent or effective resistance in series combination :-

➪ Let two resistances R1 and R2 are connected in series with a source of 'V' volt and 'I' is the current flowing in the resistance then,

(we know that , by ohm's law V = IR )

V1 = IR1

V2 = IR2

the total potential

→ V = V1 + V2

or V = IR1 + IR2

if the effective or equivalent resistance of the combination is Rs then,

${ \tt \: V = IRs } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt \implies \cancel{I}Rs = \cancel{I}(R1+R2)} </p><p> \\ \implies {\tt \: Rs = R1 + R2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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✈︎ hence, in series combination the effective resistance is equal to the sum of individual resistances.

✈︎ The effective resistance is more than the individual resistance.