Electric Circuits - Mission EC10 Detailed Help

Three resistors are connected in parallel. If placed in a circuit with a 12-Volt power supply, determine the equivalent resistance, the total circuit current, and the voltage drop across and current through each resistor. Enter your answers to the third decimal place.


 
Often times, success in physics demands that you have the proper approach - a good game plan. The following strategy should serve you well:
  1. Determine the equivalent resistance of the entire circuit. See Formula Frenzy section.
  2. Determine the current in the battery using the equivalent resistance and the battery voltage. The relationship is Ibattery = ∆Vbattery/ Req.
  3. The voltage drop across each branch is the same as that in the battery. You can quickly determine the values of ∆V1, ∆V2, and ∆V3.
  4. Use the voltage drop and the resistance of each resistor to determine the current through each individual resistor. See first Know the Law section.
  5.  As a final check, the sum of the current values in each individual branch should equal the overall current. While this check is not necessary, it is a wise habit to perform it in order to quickly catch any errors. See second Know the Law section.
 

 
For parallel circuits, the mathematical formula for computing the equivalent resistance (Req) from the resistance values of the individual resistors (R1, R2, R3, ...) is
1 / Req= 1 / R1+ 1 / R2+ 1 / R3+ ...
 

 
Branch Currents in Parallel Circuits:
The current in an individual branch of a parallel circuit is dependent upon the voltage drop across the branch and the resistance of the resistor within the branch. The voltage drop across a branch in a parallel circuit is equal to the voltage rating of the battery. Thus, the current in a branch can be calculated as
 
Ibranch= ∆Vbattery/ Rbranch


 
Current in Parallel Circuits:
Parallel circuits are characterized by branching locations. At each branching location, the current is divided into separate pathways. The overall current approaching the branch is equal to the sum of the current values in each individual branch. This can be expressed in equation form as
 
Itot= I1+ I2+ I3+ ...

where Itot is the current outside the branches (and through the battery) and I1, I2 and I3 are the current values in the individual resistors.