Question 6
How would the current through the 2 ohm resistor compare to the current through the 4 ohm
70
402
20
9v
592
D
E
One-fourth as large
One-half as large
Four times as large
Equally as large
Answers
Answer:
Components connected in parallel are connected so the same voltage is applied to each component. In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component. To find the total resistance of all components, the reciprocals of the resistances of each component is added and the reciprocal of the sum is taken. Hence, the Total resistance will always be less than the value of the smallest resistance. That is,
R
total
1
=
R
1
1
+
R
2
1
...
R
n
1
,R=R
total
−1
.
In this case, the 4 ohms and 2 ohms resistances are connected in parallel. So the total resistance will be
4
1
+
2
1
=
0.75
1
=1.33ohms.
As it is a parallel connection, the voltage across each of the components is the same, and the total current is the sum of the currents through each component.
Total voltage in the circuit is given as V = IR = 1.33 * 3 = 4 V.
Now, the current across the 2 ohms wire is given as I=V/R = 4/2 = 2A.
Hence, 2A of current passes through the 2 ohms wire.