SPRING 3072954 - Caterpillar

The circuit that is shown in Illustration 5 is a typical DC circuit with three parallel branches. The circuit also contains an ammeter connected in series with the parallel branches (all current flow in the circuit must pass through the ammeter).Applying the basic rules for parallel circuits makes solving this problem very simple. The source voltage is given (24 volts) and each branch resistance is given (R1 = 4Ohms; R2= 4Ohms; R3 = 2Ohms). Applying the voltage rule for parallel circuits (voltage is the SAME in all branches) you can solve the unknown current value in each branch by using the Ohm's Law Circle, whereas, I = E/R.I1 = E1/R1 or I1 = 24/4 or I1 = 6 ampsI2 = E2/R2 or I2 = 24/4 or I2 = 6 ampsI3 = E3/R3 or I3 = 24/2 or I3 = 12 ampsSince current flow in parallel branches is the sum of all branch currents, the equation for total current is It = I1 + I2 + I3 or 6+6+12 = 24 amp. With the source voltage given as 24 volts and the total current calculated at 24 amp, the total circuit resistance is calculated as 1 ohm. (Rt = Et/It).Series-Parallel Circuits
Illustration 6 g01070324
A series-parallel circuit is composed of a series section and a parallel section. All of the rules previously discussed regarding series circuits and parallel circuits are applicable in solving for unknown circuit values.Although some series-parallel circuits appear to be very complex, the series parallel circuits are solved quite easily by using a logical approach. The following tips will make solving series-parallel circuits less complicated:
Examine the circuit carefully. Then determine the path or paths that current may flow through the circuit before returning to the source.
Redraw a complex circuit to simplify the appearance.
When you simplify a series parallel circuit, begin at the farthest point from the voltage source. Replace the parallel resistor combinations one step at a time.
A correctly redrawn series parallel (equivalent) circuit will contain only ONE series resistor in the end.
Apply the simple series rules for determining the unknown values.
Return to the original circuit and plug in the known values. Use Ohm's Law to solve the remaining values.Solving a Series-Parallel Problem
Illustration 7 g01070325
The series parallel circuit, as shown in Illustration 7, shows a 2Ohms resistor in series with a parallel branch that contains a 6Ohms resistor and a 3Ohms resistor. To solve this problem it is necessary to determine the equivalent resistance for the parallel branch. Using the following equation, solve for the parallel equivalent (Re) resistance:1/Re = 1/R2 + 1/R31/Re = 1/6 + 1/3 or1/Re = .1666 +.3333 = .50 or1/Re = 1/.50 or Re = 2 ohmsIllustration 7 has been redrawn (See Illustration 8) with the equivalent resistance for the parallel branch. Solve circuit totals by using simple Ohm's Law rules for series circuits.
Illustration 8 g01070328
Using the rules for series circuits, the total circuit resistance can now be calculated by using the equation Rt = R1 + Re or Rt = 2 + 2 or 4 ohms.The