Derivation of formula for resistors in parallel

The voltage across each resistor is the same as the battery voltage

Animation explaining how the formula for the effective resistance of parallel circuits is derived.

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Let's see if we can derive the equation for finding the effective resistance of parallel circuits.

This is the strategy

write an equation saying: current drawn from the battery = sum of the currents through each resistor
write V/R instead of I
use the fact that the voltage across each resistor is the same as the battery voltage
divide by V all the way through since it's the same both sides, which leaves us our expression in R

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