equal to the sum of the reciprocals of the individual resistances. Example . In the circuit diagram given in Fig. .
, suppose the resistors R , R and R have the values Ω , Ω , Ω , respectively, which have been connected to a battery of V. Calculate (a) the current through each resistor, (b) the total current in the circuit, and (c) the total circuit resistance. R = Ω , R = Ω , and R = Ω . Potential difference across the battery, V = V.
This is also the potential difference across each of the individual resistor; therefore, to calculate the current in the resistors, we use Ohm’s law. The current I , through R = V/ R I = V/ Ω = . A. The current I , through R = V/ R I = V/ Ω = .
A. The current I , through R = V/R I = V/ Ω = . A. The total current in the circuit, I = I + I + I = ( .
+ . + . ) A = A The total resistance R p , is given by [Eq. ( .
)] p + + Thus, R p = Ω . Example . If in Fig. .
, R = Ω , R = Ω , R = Ω , R = Ω , R = Ω , and a V battery is connected to the arrangement. Calculate (a) the total resistance in the circuit, and (b) the total current flowing in the circuit. Suppose we replace the parallel resistors R and R by an equivalent resistor of resistance, R ′ . Similarly we replace the parallel resistors R , R and R by an equivalent single resistor of resistance R ″ .