N1 Engineering Science|The Easy Way! 109


If resistors R1, R2 and R3 are connected in parallel across a supply as shown in fig. 6.6, then applying Kirchhoff’s first law:


IT = I1 + I2 + I3 .............................................................................................................. (6.8)


Applying Ohm’s law: V


RT = V R1 + V R2 + V R3 \ VT = V1 = V2 = V3 ................................................................................................... (6.9)


Dividing by V as it is constant: 1


RT


= 1 + 1 R1


R2 + 1 Example 6.15


If the resistors of example 6.13 are connected in parallel across the same 24 V supply, calculate; (a) (b) (c) (d)


the total resistance of the circuit, the pd across each resistor,


the current through each resistor, and the total current drawn from the supply.


Solution: (a)


R3 mhos  ( “Upsilon” = omega inverted) .............................. (6.10)


RT = 1 1 = 1


1 R1 RT = 0,78  (mhos)


RT 1


\ RT = 1 (b) (c) 078, = 1,282 ohms


In a parallel circuit: VT = V1 = V2 = V3 = 24 V


I1 = V = 24


4 = 6 A (d) IT = V RT = 24 1 282, = 18,72 A R1


I2 = V = 24


6 = 4 A or in a parallel circuit R2 I3 = V R3 = 24 275, = 8,727 A


IT = I1 + I2 + I3 = 6 + 4 + 8,72


= 18,72 A


+ 1 4 + 1


R2


+ 1 6 + 1 275,


R3


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