MEL TECH
CIRCTRONICS
Series Circuit
In a series circuit, each device is connected in a manner such that there is only one pathway by which charge can traverse the external circuit. Each charge passing through the loop of the external circuit will pass through each resistor in consecutive fashion. A circuit in which the components are connected to form one conducting path.
Resistors in Series - the resistors are connected end to end.
Example:
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Assume that Vt = 60 V.
The analysis begins by using the resistance values for the individual resistors in order to determine the equivalent resistance of the circuit.
Req = R1 + R2 + R3 = 17 Ω + 12 Ω + 11 Ω = 40 Ω
Now that the equivalent resistance is known, the current at the Vt can be determined using the Ohm's law equation. In using the Ohm's law equation (V = I • R) to determine the current in the circuit, it is important to use the battery voltage for V and the equivalent resistance for R. The calculation is shown here:
Itot = Vt / Req = (60 V) / (40 Ω) = 1.5 amp
The 1.5 amp value for current is the current at the Vt location. For a series circuit with no branching locations, the current is everywhere the same. The current at the Vt location is the same as the current at each resistor location. Subsequently, the 1.5 amp is the value of I1, I2, and I3.
Vt = I1 = I2 = I3 = 1.5 amp
There are three values left to be determined - the voltage drops across each of the individual resistors. Ohm's law is used once more to determine the voltage drops for each resistor - it is simply the product of the current at each resistor (calculated above as 1.5 amp) and the resistance of each resistor (given in the problem statement). The calculations are shown below.
|
V1 = I1 R1 V1 = (1.5 A) (17 Ω ) V1 = 25.5 V |
V2 = I2 R2 V2 = (1.5 A) (12 Ω ) V2 = 18 V |
V3 = I3 R3 V3 = (1.5 A) (11 Ω ) V3 = 16.5 V |
As a check of the accuracy of the mathematics performed, it is wise to see if the calculated values satisfy the principle that the sum of the voltage drops for each individual resistor is equal to the voltage rating of the battery. In other words,
is Vt = V1 + V2 + V3 ?
Is 60 V = 25.5 V + 18 V + 16.5 V ?
Is 60 V = 60 V?
Check!!!
Parallel Cicuit
In a parallel circuit, each device is placed in its own separate branch. The presence of branch lines means that there are multiple pathways by which charge can traverse the external circuit. Each charge passing through the loop of the external circuit will pass through a single resistor present in a single branch. When arriving at the branching location or node, a charge makes a choice as to which branch to travel through on its journey back to the low potential terminal.
Resistors in Parallel - the resistors are connected across each other.
1. The total current in a parallel circuit is equal to the sum of the currents in the separate branches.
It = I1 + I2 + I3...
2. The potential difference across across all branches of a parallel circuit must have the same magnitude.
V - V1 - V2 = V3 =...
3. The reciprocal of the equivalent resisitance is equal to the sum of the reciprocals of the separate resistances in parallel.
_1_ = _1 + 1_ + _1_ ...
R R1 R2 R3
Example:
Rt = _______1__________
(1/R1) + (1/R2)...
Since R1 = 20 Ω and R2 = 30 Ω,
Rt = _______1__________
(1/20Ω) + (1/30Ω)
Rt = 12Ω