prove
that
Rs = R1 + R2 + R3
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Let R₁ , R₂ and R₃ be three resistors in series
V₁ , V₂ , V₃ be potential difference across R₁ , R₂ , R₃ respectively
I be the current through all three resistors
The sum of individual voltages across each resistor will be the total voltage,
Vs = V₁ + V₂ + V₃
We know that, from Ohm's Law
V = IR
Hence,
Vs = V₁ + V₂ + V₃
IRs = IR₁ + IR₂ + IR₃
IRs = I(R₁ + R₂ + R₃)
Rs = R₁ + R₂ + R₃
Hence proved
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