Mission EC7 Series Circuits Concepts

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Three identical light bulbs are connected to a battery as shown below. W, X,Y and Z represent locations along the circuit. Which one of the following statements is true?

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

∆V_tot= ∆V₁+ ∆V₂+ ∆V₃+ ...

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

This question asks you to make comparisons of voltage drops between various sets of locations on a series circuit which are on opposite sides of one or more resistors. As discussed in the Know the Law and Formula Frenzy sections, the voltage drops between two locations is dependent upon the current at that location and the resistance of the resistors between those two locations. The current is the same at all locations so the determining factor is the resistance value. The light bulbs are identical so they have the same resistance value. Thus, the voltage drop across a single bulb will be the same for any one of the bulbs. And the voltage drop across two bulbs or three bulbs will be greater than the voltage drop across a single bulb. Successfully answering this question demands that you carefully analyze the two listed locations to determine if they are separated by one bulb, two bulbs or three bulbs.

How can one determine the electric potential difference between two points or across a single resistor on a series circuit?