Circuit : Andy Collinson
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Example 1
Using the techniques of Ohm's law and Kirchoff's law currents I1 and I2 can be found and the value of resistor R, in the diagram above.
The voltage across points A to B
On the right hand loop,
Vab
10
-6
I2 = 6 + I3 * 2 = 10V
= 16 - 4*I2
= 16 - 4*I2
= -4 *I2
= 1.5 amp
On the right hand loop,
Vab
10
-6
I2 = 6 + I3 * 2 = 10V
= 16 - 4*I2
= 16 - 4*I2
= -4 *I2
= 1.5 amp
On the left hand loop Vab = 12 - R*I1
The sign of the voltages is given by the polarity rule ( current flowing into a resistor develops a p.d.positive on the side where the arrow points in.) Using Kirchoff's current law for I1 :
I1 + I2 = I3 therefore I1 = I3 - I2 = 0.5 amp
On the left hand loop,
Therefore :
Therefore :
Vab
10
R
10
R
= 12 - R * 0.5
= 12 - R * 0.5
= 2/0.5 = 4ohms
= 12 - R * 0.5
= 2/0.5 = 4ohms
A quick check can be performed using a simulator program. Alternatively you could use Kirchoff's voltage law on the left hand loop.