The expression for the equivalent resistance of the combination of resistors R1, R2 and R3 in a series combination is__

A
$R_{s} = R_{1} + R_{2} + R_{3}$
B
$\frac{1}{R_{s}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$
C
Both 1 and 2
D
None of the above

Solution:

The expression for the equivalent resistance of the combination of resistors

R_{1}, R_{2} and R_{3}

in a series combination is

R_{s} = R_{1} + R_{2} + R_{3} .

Given the resistors

, R_{1}, R_{2} and R_{3}

are connected in series with a battery, key, and the ammeter connected. The current I flows through the circuit. The current remains the unchanged in series combination.
Let the voltage (potential difference) across each resistance be

V

.
Using Ohm's law we have

V_{1} = I R_{1}; V_{2} = I R_{2} and V_{3} = I R_{3}

Total potential difference across the circuit

V_{s} = V_{1} + V_{2} + V_{3}

I R_{s} = I R_{1} + I R_{2} + I R_{3}

Therefore

R_{s} = R_{1} + R_{2} + R_{3}

Here in a series combination of resistors, the equivalent resistance is equal to the sum of the individual resistances.

https://lh6.googleusercontent.com/xF7Bkg2Xv0-YtJHDBp2jZAdaqBeBkiY_wyXsBuNaG2K6Lxxwi6Uzea7W4ekgBRR602HyjXCJm7ZxcNe2gdVtNXaVbFvmeBar5MV9RVB394Mo0vrCFjWNEI5VStwz7j1BPb67eCSxsuOD5XdUyibz7hqizkDUQqOSF5CJ9QOwdorbIaOxHKTEOcwjhHqdzMsLxLDf2g

The expression for the equivalent resistance of the combination of resistors $R_{1}, R_{2}$ and $R_{3}$ in a series combination is__

Solution:

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