Question

Three students are having a conversation. It goes like this. Allison says: "This problem says, can you add a resistor to the circuit so that the current provided to the circuit by the battery increases. How is that possible? For the current to increase, the overall resistance of the circuit has to decrease. Doesn't adding a resistor always increase the resistance of the circuit?" Nima says: "Let's try putting the resistor in series with the other resistors. Look, it doesn't matter where we put it, adding it in series always increases the resistance of the circuit, and that decreases the current." Natasha says: "That's absolutely right. However, what if we placed the new resistor in parallel with one of the others. Look, if we do that, the resistance of that part of the circuit goes down. That has to increase the current from the battery."Which of the students are absolutely correct here?

Answer 1

Answer:

Nima and Natasha are absolutely correct.

Explanation:

When connecting two resistors in series, their resistances add:

$R_{eq}=R_{1}+R_{2}$

which means that whenever we add a resistance in series, their magnitudes will add, giving us a resistance that is greater than the original resistance, which will demand less current from the battery because of ohm's law:

$I=\frac{V}{R}$

So, the greater the resistance, the smaller the current.

When connecting two resistors in parallel, the reciprocal of ther resistances add:

$\frac{1}{R_{eq}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$

or

$R_{eq}=\frac{R_{1}R_{2}}{R_{1}+R_{2}}$

The equivalent resistance will always be less than the smallest resistor in the circuit, so the equivalent resistance will always decrease as more resistors are added. A decrease in the resistance means that the current will increase.