) Resistors connected in parallel have the same potential difference across them, with different currents (generally speaking). Imagine a current I flowing into a junction and splitting into currents I_(1) and I_(2) (where I_(1)+I_(2)=I) which flow through resistors R_(1) and R_(2), respectively. If R_(1) and R_(2) are connected in parallel (V_(1))=(V_(2)), show that one could replace the two of them with an equivalent resistor R_(eq) such that
(1)/(R_(eq))=(1)/(R_(1))+(1)/(R_(2))
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a) Resistors connected in parallel have the same potential difference across them, with different currents (generally speaking). Imagine a current I flowing into a junction and splitting into currents I_(1) and I_(2) (where I_(1)+I_(2)=I) which flow through resistors R_(1) and R_(2), respectively. If R_(1) and R_(2) are connected in parallel (V_(1))=(V_(2)), show that one could replace the two of them with an equivalent resistor R_(eq) such that
(1)/(R_(eq))=(1)/(R_(1))+(1)/(R_(2))