Electric Circuits - Mission EC7 Detailed Help

Compare circuit X and Y below. Each are powered by a 12-volt battery. The voltage drop across the 12-ohm resistor in circuit Y is ____ the voltage drop across the single resistor in X.

Voltage Drops in a Series Circuit:
Electric charge encounters an energy gain as it passes through the battery. This energy boost means that it also encounters an increase in electric potential. The amount of electric potential difference between the two terminals of the battery is equal to the voltage rating on the battery. The gain in electric potential made in the battery is lost by the charge when making the loop around the external circuit. In series circuits, this loss occurs in a stepwise fashion as the charge passes through each resistor. The sum of the voltage drops across each resistor is equal to the voltage rating of the battery. The voltage drop (V) across an individual resistor within a series circuit can be determined from the resistance of the resistor (R) and the current (I) in the circuit. For example:

V1= I • R1          ∆V2= I • R2

For series circuits, the mathematical formula that compares the voltage rating of the battery (Vtot) to the voltage drops across the individual resistors (V1V2V3, ...) is
Vtot= ∆V1+ ∆V2+ ∆V3+ ...

This question asks you to compare the voltage drops across individual resistors in two different circuits. Circuit Y consists of two resistor connected in series. The voltage drop across either one of the resistors must be less than the battery voltage. See Know the Law and Formula Frenzy sections. Circuit X consists of a single resistor. The voltage drop in this resistor is equal to the battery voltage.


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