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The current drawn by the series circuit is(R₁ + R₂)/R₁R₂ times the current drawn by the parallel circuit.
Let the resistance of the two lamps are R₁ and R₂.
Then the equivalent resistance in series combination is: R = R₁ + R₂.
And, the equivalent resistance in parallel combination is:
r = R₁R₂/(R₁ + R₂).
So, if the supply voltage is V,
Then, current drown in series combination; = V/R = V/(R₁ + R₂)
And, current drown in parallel combination; = V/r = V(R₁ + R₂)/R₁R₂
So , = [ V/(R₁ + R₂)] /[V(R₁ + R₂)/R₁R₂]
= (R₁ + R₂)/R₁R₂
Hence, the ratio of current drawn in series and current drown in parallel is (R₁ + R₂)/R₁R₂. So, he current drawn by the series circuit is(R₁ + R₂)/R₁R₂ times the current drawn by the parallel circuit.
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