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Q.

The expression for equivalent resistance of two resistors $R_{1}$ and $R_{2}$ connected in series is {fill_ regular}.

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Detailed Solution

The expression for equivalent resistance of two resistors

R_{1}

and

R_{2}

connected in series is

R_{1} + R_{2}

.
The total potential difference across a series of resistors equals the sum of the individual resistor potential differences. For example, if two resistors are connected in series via voltage source V, then the total resistance (R) in the circuit is-

= > V = V_{1} + V_{2}

………………………… (i)
When we apply Ohm's law to the complete circuit, we get

= > V = I R

[

V = voltage; I = current; R = resistance]

When we apply Ohm's law to the three resistors separately, we get

= > V_{1} = I R_{1}

[

V_{1} = voltage across; resistance 1; R_{1} = first resistance]

…….. (ii)

= > V_{2} = I R_{2}

[

V_{2} = voltage across; resistance 1; R_{1} = second  resistance]

…….. (iii)
Put the values of equation (ii) and (iii) in (i) we get

= > IR = I R_{1} + I R_{1}

= > IR = I (R_{1} + R_{1})

= > R_{s} = R_{1} + R_{2}

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The expression for equivalent resistance of two resistors R1 and R2 connected in series is {fill_ regular}.