# Equivalent Resistance (Prep for Lab on DC circuits)

• TheOculus
In summary, the equivalent resistance of the circuit with R1 = 5, R2 = 5, R3 = 4, R4 = 5, R5 = 1 and R6 = 2, with a 2 V battery and the switch closed, is 1.43 Ω. The resistors R_4 and R_6 are in parallel, and their equivalent resistance is in series with the rest of the resistors.
TheOculus

## Homework Statement

Use the circuit shown to answer the following questions. At time t = 0 the switch in the circuit is closed. Answer the following questions after the switch in the circuit is closed.

What is the equivalent resistance of the circuit given R1 = 5 , R2 = 5 , R3 = 4 , R4 = 5 , R5 = 1 and R6 = 2 and a 2 V battery?

## Homework Equations

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+...$ for parallel
$R_{eq}=R_1+R_2+...+R_n$ for series

## The Attempt at a Solution

Alright, this didn't seem too complicated to me but all of my attempts have resulted in incorrect answers. The way I am seeing it is that $R_4$ and $R_6$ are parallel, and that the equivalent resistance of these two resistors are in series with the rest of the resistors. Here's my attempt:

$\frac{1}{R_{46}}=\frac{1}{5}+\frac{1}{2}=0.7Ω$ Now, the reciprocal of this is ≈1.43Ω which gives the equivalent resistance of resistors 4 and 6.
It seems like a simple matter here to add up this equivalent resistance to the rest of the resistors in series: 1.43+5+5+4+1=16.43Ω

Am I incorrect in my parallel/series diagnosis? I have tried several other options, which I won't type up here, but if my diagnosis is wrong I will offer up my other thoughts. Thanks in advance.

TheOculus said:
The way I am seeing it is that $R_4$ and $R_6$ are parallel, and that the equivalent resistance of these two resistors are in series with the rest of the resistors.

No, the equivalent of R_3, R_4 and R_5 is in parallel with R_6.

Recalculating. Hadn't seen a resistor setup like that. I'm not sure I understand why they are in parallel. Is it because there is no wire between, i.e. they are connected to each other?Edit: Ok, that worked like a charm. Thanks.

## 1. What is equivalent resistance?

Equivalent resistance is the total resistance of a circuit, which is measured in Ohms (Ω). It takes into account all the resistors in a circuit and represents the total resistance that a single resistor would have if it replaced all the other resistors in the circuit.

## 2. How is equivalent resistance calculated?

Equivalent resistance is calculated using Ohm's law, which states that resistance is equal to the voltage (V) divided by the current (I). In parallel circuits, the equivalent resistance is calculated by adding the reciprocals of the individual resistances and then taking the reciprocal of the sum. In series circuits, the equivalent resistance is calculated by adding all the individual resistances together.

## 3. Why is equivalent resistance important?

Equivalent resistance is important because it helps simplify complex circuits into a single equivalent resistor. This makes it easier to analyze and understand the circuit's behavior and to calculate the current and voltage in the circuit.

## 4. How does equivalent resistance affect the current and voltage in a circuit?

In a series circuit, the equivalent resistance will increase as more resistors are added, which decreases the overall current in the circuit. In a parallel circuit, the equivalent resistance will decrease as more resistors are added, which increases the overall current in the circuit. The voltage across each resistor will remain the same in a series circuit, but in a parallel circuit, the voltage across each resistor will be equal to the total voltage in the circuit.

## 5. Can equivalent resistance be greater than the largest individual resistance in a circuit?

Yes, in a parallel circuit, the equivalent resistance can be less than the smallest individual resistance, and in a series circuit, the equivalent resistance can be greater than the largest individual resistance. This is because the total resistance in a circuit is affected by the way resistors are connected, whether in series or in parallel.

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