the current I through the circuit remains the same. Applying Ohm’s law to the entire circuit we have, V=IR On applying ohm’s law to the three resistors separately we further have V1 = IR1, V2 = IR2 and V3 = IR3 Substituting these values in equation (1)
Resistors in parallel Consider three resistors having resistances R1, R2, R3 connected in parallel. This combination is connected with a battery and plug key as shown in Fig. 16.5 In parallel combination the potential difference across each resistor is the same having a value V. The total current I is equal to the sum of the separate currents through each branch of the combination. I = I1+I2+I3
IR = IR1+IR2+IR3 (or)
(1)
Let Rp be the equivalent resistance of
Rs = R1+R2+R3
When several resistors are connected in series, the resistance of the combination Rs is equal to the sum of their individual resistances R1, R2, R3 and is thus greater than any individual resistance. Example 16.4 Two resistances 18 Ω and 6 Ω are connected to a 6 V battery in series. CalcuFig. 16.5 late (a) the total resistance of the circuit, the parallel combination of resistors. By (b) the current through the circuit. applying Ohm’s law to the parallel combiSolution: nation of resistors we have I = V/Rp (a) Given the resistance, R1 = 18 Ω R2 = 6 Ω
On applying ohm’s law to each resistor We have I1 = V/R1, I2 = V/R2 and I3 = V/R3
The total resistance of the circuit RS= R1+R2
Substituting these values in equation (1)
RS = 18 Ω + 6 Ω = 24 Ω
PHYSICS
(b) The potential difference across the two terminals of the battery V = 6 V Now the current through the circuit, I = V/ RS = 6 V / 24 Ω = 0.25 A
V/Rp = V/R1+V/R2+V/R3 (or)
1/Rp = 1/R1+1/R2+1/R3
Thus the reciprocal of the equivalent resistance of a group of resistance joined in parallel is equal to the sum of the reciprocals of the individual resistance.
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