What Happens When You Remove a Resistor from a Parallel Circuit?

In a parallel circuit, what is the expected effect on the total resistance if all resistors are of equal value and one is removed?

• A. Total resistance will increase
• B. Total resistance will decrease
• C. Total resistance will remain the same
• D. Total resistance will become infinite

Answer: (A)

In a parallel circuit, the total resistance is determined by the reciprocal of the sum of the reciprocals of each individual resistor's resistance. When all resistors are of equal value, the formula for the total resistance becomes: 1/R_total = 1/R + 1/R + ... + 1/R (for the number of resistors, n). This simplifies to: R_total = R/n, where R is the resistance of one resistor, and n is the number of resistors. If one resistor is removed from this parallel configuration, the total number of resistors decreases from n to n-1. Therefore, the new total resistance can be computed as: R_new_total = R/(n-1). As the value of n decreases, the denominator (n - 1) becomes smaller, resulting in a larger value for R_new_total compared to R_total. Hence, the total resistance increases when a resistor is removed from one of all equal value in a parallel circuit. This is because, with fewer pathways for current to flow, the overall ability for the circuit to conduct electricity diminishes, leading to a higher total resistance. Thus, the correct response reflects this understanding of how parallel circuits behave when resistive components are removed.

What Happens When You Remove a Resistor from a Parallel Circuit?

You might have come across parallel circuits in your science classes, and believed me when I say, they can be both fascinating and a bit perplexing! If you’re grappling with concepts of resistance, particularly what occurs when you yank a resistor out of a parallel circuit filled with equally valued resistors, then you’re in for a solid understanding.

Let’s Break It Down - Parallel Circuits 101

In a parallel circuit, all resistors share the same voltage, but the current can flow through multiple paths. To find the total resistance, we use the formula:

1/R_total = 1/R + 1/R + ... + 1/R (for n resistors)

When all resistors are equal, you can simplify it to:

R_total = R/n

Where R is the resistance of a single resistor and n is the number of resistors. Easy enough, right?

Now, imagine you have four identical resistors in your circuit. If one suddenly goes missing, how does that impact the total resistance? It’s a little like friends leaving a party—fewer friends mean a quieter gathering!

The Effect of Removing a Resistor

When you remove one resistor from your setup, you change the number of resistors from n to n-1. So now, your new total resistance formula looks like:

R_new_total = R/(n-1)

In this scenario, let's say you started with four resistors, which makes the original total resistance R_total = R/4. After one is removed, you’re left with three, thus R_new_total = R/3.

Wait, What Just Happened?

At first glance, it may seem counterintuitive that removing a pathway for current flow could lead to an increase in resistance. But hear me out! When you have fewer resistors, there are fewer paths for the current to navigate. This reduced ability to carry current means the overall resistance increases—yes, you heard that right.

It's like trying to squeeze through a crowded hallway with friends—more people get in the way and make it harder to move. Similarly, fewer pathways mean less ease of flow for the current, thus raising the total resistance.

So, To Sum It Up

When you're handling a parallel circuit and remove one of the resistors (especially when they’re all equal), you’re left with a higher total resistance. It can be a bit of a mental leap, but understanding that the fewer the pathways, the harder it is for the electrical current to flow can help solidify this concept. The takeaway? Remove a friend from the party, and things get a tad quieter—reduce the number of paths in your parallel circuit, and resistance increases!

Understanding these principles is crucial not just for exams but for comprehending how electrical systems function in real life. So, the next time you find yourself pondering over your circuit theory or preparing for your Medical College Admission Test, remember this insightful piece of information! Knowledge is power, after all!