Electric Circuits - Mission EC7 Detailed Help

A 12-V battery and a 12-ohm resistor are connected as shown in circuit X below. Two 12-ohm resistors are connected as shown in circuit Y. The current in the battery in circuit X is ____ that in the battery in circuit Y.


 
Current in a Series Circuit:
The overall current in a series circuit is no different than the current in an individual resistor. That is, the current in the battery is the same as the current in resistor 1 or resistor 2 or resistor 3 or ... . Since there are no branching locations, current is never divided and is everywhere the same. The amount of current is related to the voltage (∆Vtot) impressed across the circuit by the battery and the overall equivalent resistance (Req). In equation form, these ideas can be written as
Itot= I1= I2= I3= ∆Vtot/ Req

 


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


 
This question asks you to make a comparison of the current in circuit X to the current in circuit Y. It is not important that the question identifies the location of the current for which the comparison is to be made. Current within a series circuit is everywhere the same. This current is dependent upon the battery voltage (direct effect) and the overall resistance (inverse effect). See Know the Law section. The battery voltage is the same for each circuit (12 V). The overall resistance will be different since the two circuits have a different number of resistors. The overall resistance will increase as more resistors are added together. This explains why circuit Y has a greater overall resistance and a smaller current. See Formula Frenzy section.