19.3 CHAPTER 19. ELECTRIC CIRCUITS
Also, from applying Ohm’s Law to the entire circuit, we can write:
V =
I
Rpwhere Rpis the equivalent resistance in this parallel arrangement.
We are now ready to apply Ohm’s Law to eachresistor, to get:
V 1 = R 1 · I 1
V 2 = R 2 · I 2
V 3 = R 3 · I 3
This can be also writtenas:
I 1 =
V 1
R 1
I 2 =
V 2
R 2
I 3 =
V 3
R 3
Now we have:
I = I 1 + I 2 + I 3
V
Rp=
V 1
R 1
+
V 2
R 2
+
V 3
R 3
=
V
R 1
+
V
R 2
+
V
R 3
because V = V 1 = V 2 = V 3= V�
1
R 1
+
1
R 2
+
1
R 3
�
∴
1
Rp=
�
1
R 1
+
1
R 2
+
1
R 3
�
DEFINITION: Equivalent resistance ina parallel circuit,Rp
For n resistors in parallel, theequivalent resistance is:1
Rp=
�
1
R 1
+
1
R 2
+
1
R 3
+··· +
1
Rn�
Let us apply this formulato the following circuit.
V =9 V R 1 =10Ω R 2 =2Ω R 3 =1Ω
What is the total resistance in the circuit?