When resistances are connected in series, the equivalent resistances is equal to:

Explanation

Resistors are said to be in series when equal current flows through each resistor because there is only one path for the charges to flow through. The equivalent resistance of a set of resistors in a series connection is equal to the algebraic sum of each individual resistance. Since the current is constant and the voltage is equal to the potential energy per charge, the sum of the voltage applied to the circuit by the source and the potential drops across the individual resistors around a loop should be equal to zero according to Kirchoff's loop law. V=V1- V2-V3 = 0 = V = V1+V2+V3 = V = IR1+ IR2+IR3 = I = v/ R1+ R2+R3 = V/Req Hence If n resistors are connected in series, the equivalent resistance is given by: Req = R1+R2+R3+Rn B. When resistances are connected in parallel, the equivalent resistance is equal to the sum of the reciprocal of individual resistances. As the voltage across each resistor remains constant and the current splits across each resistor according to Kirchoff's junction rule. Hence the equivalent resistance in this case is the sum of the reciprocal of individual resistances. I = I1+I2 =V1/R1 + V2/R2 = V/R1 + V/R2 = V ( 1/R1+ 1/R2) = V/Req =1/Req = (1/R1+ 1/R2)