Electric Circuits - Mission EC11 Detailed Help

Three resistors are connected to a 12-Volt power supply to form a combination circuit. Two of the resistors (R1 and R2) are connected in parallel branches while the third resistor (R3) is connected outside the branches. Determine the equivalent resistance and the current through each resistor. Enter your answers to the third decimal place.

 
 
Definition of a Combination Circuit:
A combination circuit is a circuit in which there are both series and parallel connections. Some of the resistors are connected in parallel to each other and the remaining resistors are connected in series to each other and in series to the parallel section.


 
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 parallel section of the circuit. If necessary, see Formula Frenzy section.
  2. Once you have determined the equivalent resistance of the branched (parallel) section, you can imagine that section being removed from the circuit and being replaced by a single resistor of that resistance. Use this concept to determine the equivalent resistance of the entire circuit (which has now been transformed by your mind into a series circuit). See Formula Frenzy section.
  3. Determine the current in the battery using the equivalent resistance of the entire circuit and the battery voltage. The relationship is     Ibattery= ∆Vbattery/Req.
  4. The current at the battery location is the same as the current at the resistor outside of the branches (I3).
  5. With I3 and R3 known, you can calculate ∆V3. You will need to know ∆V3 in order to calculate the voltage drop across the branches. Record the ∆V3 and the ∆Vbranches to several decimal places (to avoid severe rounding). Refer to the Know the Law section.
  6. Use the resistance of each branch resistor and the ∆Vbranches to determine the current in the two branch resistors.


 
The equivalent resistance of a section of parallel connected resistors (R1 and R2) can be calculated using the equation   
  
1/Req= 1/R1+ 1/R2+ ...


The equivalent resistance of a section of series connected resistors (R3 and R4) can be calculated using the equation   
  
Req= R3+ R4+ ...
 

 
Voltage Drops in a Combination Circuit:
Charge gains energy (and electric potential) in the battery and loses energy (and electric potential) in the external circuit. The amount of electric potential gain in the battery is equal to the amount of loss in the external circuit. For combination circuits, this loss occurs in a stepwise fashion as the charge passes through each resistor. A single charge only passes through one of the resistors in a parallel branch. Thus, the voltage drop across either one of the parallel resistors plus the sum of the voltage drops across each series resistor is equal to the voltage rating of the battery. The voltage drop across an individual resistor within a series circuit can be determined from the resistance of the resistor and the current through the circuit. For example:

∆V1= I1•R1          ∆V2= I2•R2          ∆V3= I3•R3