Electric Circuits - Mission EC7 Detailed Help

Consider circuits X and Y below. Each circuit is powered by the same battery and contains identical resistors. Circuit X has one resistor and circuit Y has two resistors. The equivalent resistance of circuit X will be ____ that of circuit Y. The current in the battery in X will be ____ that in the battery in Y. Enter the two answers ... .

Definition of Equivalent Resistance:
The equivalent resistance of a circuit is the amount of resistance which a single resistor would need in order to equal the overall effect of the collection of resistors which are present in the circuit.

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

R_eq= R₁+ R₂+ R₃+ ...

The difference between circuit X and circuit Y is that circuit Y has more resistors than circuit X. The extra resistor in circuit Y is connected in series. The effect of the extra resistor on the overall or equivalent resistance of circuit Y is seen in the equation above in the Formula Frenzy section. Adding more resistors in series increases the overall resistance. The current in a circuit is directly related to the battery voltage (∆V) and inversely related to the equivalent resistance (R_eq). See the Know the Law section. Thus, an increase in the equivalent resistance would lead to a decrease in the current in the battery.

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 (∆V_tot) impressed across the circuit by the battery and the overall equivalent resistance (R_eq). In equation form, these ideas can be written as

I_tot= I₁= I₂= I₃= ∆V_tot/ R_eq.

How does an increase in the number of series-connected resistors effect the overall resistance and the current in the battery?

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