The same voltage V is impressed on each of the branches of a parallel circuit. T

Question

The same voltage V is impressed on each of the branches of a parallel circuit. The voltage source provides a total current I total to the circuit and "sees" a total equivalent resistance of Req in the circuit. That is, V=ItotalReq. The total current is equal to the sum of the currents through each branch of the parallel circuit. In a circuit with nbranches, Itotal=I1+I2+I3++In.

Part A

Use Ohm's law (I=V/R) and find the equivalent resistance of a parallel circuit with n branches.

The same voltage V is impressed on each of the branches of a parallel circuit. The voltage source provides a total current I total to the circuit and "sees" a total equivalent resistance of Req in the circuit. That is, V=ItotalReq. The total current is equal to the sum of the currents through each branch of the parallel circuit. In a circuit with nbranches, Itotal=I1+I2+I3++In.

Part A

Use Ohm's law (I=V/R) and find the equivalent resistance of a parallel circuit with n branches.

Use Ohm's law  and find the equivalent resistance of a parallel circuit with  branches. 1/Req=1/R1+1/R2+1/R3++1/Rn 1/Req=R1+1/R2+R3++1/Rn 1/Req=1/R1+1/R21/R3+1/Rn Req=R1+R2+R3++Rn

Explanation / Answer

given

voltage is V

current is i and for the n branches

total current is itotal = i1 + i2 + ..... + in   

using Ohm's law

we have V = itotal X Req  

then the equivalent resistance of a parallel circuit with n branches is

1 / Req = 1 / R1 + 1 / R2 + 1 / R3 + ............ + 1 / Rn

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