Page 103 - Physics 10_Float

CURRENT ELECTRICITY

Thus, Eq.14.9 becomes

V V V
I = + +
R 1 R 2 R 3
1 1 1
I = V ( + + ) ......... (14.10)

R 1 R 2 R 3
We can replace the combination of resistors with a single
resistor called the equivalent resistance R such that the For your information
e
same current passes through the circuit. From Ohm's law
current 3 A 2 A
I = V/R Thus, Eq. 14.10 becomes
e .
1 A 1 A 1 A
V 1 1 1
R = V R + R + R
e 1 2 3
1 1 1 1
= + ......... (14.11)
+
R e R 1 R 2 R 3
Thus, the reciprocal of equivalent resistance of a parallel In parallel circuit current
divides into branches.
combination is sum of the reciprocals of the individual
resistances, which is less than the smallest resistance of the
combination. If resistances R , R , R …...., R are connected in ,
1 2 3 n
parallel, then the equivalent resistance of the combination
will be given by
1 1 1 1 1
R = R + R + R +.........+ R
e 1 2 3 n
Parallel circuits have two big advantages over series circuits.
1. Each device in the circuit receives the full battery voltage.
2. Each device in the circuit may be turned off independently
without stopping the current flowing to the other devices in
the circuit. This principle is used in household wiring.

Example 14.5: If in the circuit (Fig. 14.13), R = 2 Ω, R = 3 Ω,
2
1
R = 6 Ω, and V= 6 V, then find the following quantities:
3
(a) equivalent resistance of the circuit.
(b) current passing through each resistance. For your information
A circuit diagram is a symbolic
(c) The total current of the circuit. method of describing a real
Solution: (a) As the resistors are connected in parallel, circuit. The electric symbols
equivalent resistance of the combination is give byR used in circuit diagrams are
e
standard, so anyone familiar
1 1 1 1 with electricity can interpret a
= + +
R e R 1 R 2 R 3 circuit diagram.

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