Why is it important to classify circuits as series or parallel?

• Sunwoo Bae
In summary, the conversation discusses the concept of series circuits and how they are defined by the flow of current through multiple components in a single path. It also addresses a mistake in the question regarding the calculation of power delivered to a circuit with corrosion. The conversation also mentions the possibility of circuits that cannot be classified as series or parallel.
Sunwoo Bae
Homework Statement
The performance of the starter circuit in an automobile can be significantly degraded by a small amount of corrosion on a battery terminal. Figure 26-38a depicts a properly functioning circuit with a battery (12.5-V emf, 0,02 ohms internal resistance) attached via corrosion-free cables to a starter motor of resistance Rs = 0.15 ohms. Suppose that later, corrosion between a battery terminal and a starter cable introduces an extra series resistance of just Rc = 0.10 ohms into the circuit as suggested in figure. Let P_0 be the power delivered to the starter in the circuit free of corrosion, and let P be the power delivered to the circuit with corrosion. Determine P/P0.
Relevant Equations
Resistors in parallel/ Resistors in series

The answer sheet assumes that the resistors in both circuits are in series and that we need to use the equation Req = R1+R2+R3.. to find the Req in both cases. How come the resistors are in series, when there are multiple resistors in a single row?

Also, why does the following work yield the wrong answer? The answer should be 0.4, but I keep getting 0.63..

Sunwoo Bae said:
How come the resistors are in series,
Because the current flowing through all of them is the same.

You need to calculate the power delivered to "the starter". Is it the same as what you have calculated?

Steve4Physics
I'd like to add to what @cnh1995 has said.

Components are in series when connected one after the other, in a simple 'chain'. All the current leaving a component enters the next component in the chain. So the current is never split.

There is a mistake in the question.
Sunwoo Bae said:
... and let P be the power delivered to the circuit with corrosion.
It should say:
"... and let P be the power delivered to the starter in the circuit with corrosion."

phinds
Sunwoo Bae said:
How come the resistors are in series, when there are multiple resistors in a single row?
Uh ... 'cause that's the DEFINITION of series?

Hi Sunwoo Bae,

If the current flows through your components in a single loop or a single path then it is a series circuit.
If the current flows through your components in two or more loops or paths then it is a parallel circuit.

Think of it as if you are walking through a forest, if :
1- There's only one path = series (for all components along that path)
2- There are multiple paths = parallel (for the components on that are on different paths)

GJ

Guy Joel R said:
Hi Sunwoo Bae,

If the current flows through your components in a single loop or a single path then it is a series circuit.
If the current flows through your components in two or more loops or paths then it is a parallel circuit.

Think of it as if you are walking through a forest, if :
1- There's only one path = series (for all components along that path)
2- There are multiple paths = parallel (for the components on that are on different paths)
Hi @Guy Joel R. Welcome to PF!

In case you hadn't noticed, this is an old thread, dating back to February!

It may also be worth noting that not all circuits can be claasified as series or parallel or some combination of these - the classic example being a bridge circuit.

1. What is Req in a DC circuit?

Req, also known as equivalent resistance, is the single resistance value that can replace multiple resistors in a circuit without changing the circuit's behavior. It is calculated using Ohm's Law and is measured in ohms (Ω).

2. How do you calculate Req in a DC circuit?

To calculate Req, you need to add all the resistances in the circuit together. If the resistors are connected in series, you can simply add them up. If they are connected in parallel, you can use the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn. Once you have the total resistance, you have found the Req for the circuit.

3. What is the purpose of finding Req in a DC circuit?

Finding Req allows us to simplify complex circuits and make calculations easier. It also helps us understand the behavior of a circuit and how changing the resistance affects the flow of current. In practical applications, knowing the Req can help us choose the appropriate components for a circuit.

4. How does Req affect the current and voltage in a DC circuit?

According to Ohm's Law, the current (I) in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance (R). This means that as the resistance (Req) increases, the current decreases, and vice versa. Similarly, the voltage across a resistor is directly proportional to the resistance, so as Req increases, the voltage also increases.

5. Can Req be negative in a DC circuit?

No, Req cannot be negative in a DC circuit. Resistance is a physical property that cannot have a negative value. If you get a negative value for Req, it means there was an error in your calculation or you have a faulty component in your circuit.

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