Find the expression for Power in circuit

In summary, the conversation discusses calculating the resistance in series, using the formula Req= R+ R= 2R. The voltage across 2R is the terminal voltage V and the expression for this is also discussed. The formula P=I^2*R is mentioned and its use in calculating the current and power is explained. It is noted that this formula yields the same result as the previous calculation. The conversation ends with the suggestion of using the formula P=IR, which also yields the same result as the previous calculations.
  • #1
VitaminK
46
4
Homework Statement
Find the expression for Power in a Circuit with two light bulbs ( each with resistance R) in series. The terminal voltage is V.
Relevant Equations
Req= R1+ R2
P=V^2/R
I was wondering if someone could check my answer and see if it is correct.
The resistance in series is Req= R+ R= 2R

1583839565324.png
1583838844231.png


The voltage across 2R is the terminal voltage V. The expression I get is:
1583839080552.png

Can I also use this formula P=I^2*R?
When using it I get:
Current through the resistors is
1583839926673.png

The resistance in series is Req= R+ R= 2R
The Power is:
1583840214428.png

However i don't get the same answer :(
 
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  • #2
Actually, you do get the same answer. ## \frac{V1^2\times 2}{R} = \frac {V^2}{2R}##

But why do the second calculation for just one lamp?
If you do the same as your first calculation for both lamps, 2R, you get a simpler answer.
But it is exactly the same as the first result!

You could also use P=IR and again get the same result.
It's hardly surprising: all you know is V and R, so you can't do better than P in terms of V and R.
 
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Likes VitaminK

Related to Find the expression for Power in circuit

What is power in a circuit?

Power in a circuit is the rate at which energy is transferred or consumed. It is measured in watts (W) and is calculated by multiplying the voltage (V) by the current (I).

What is the formula for calculating power in a circuit?

The formula for calculating power in a circuit is P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes.

How is power related to voltage and current in a circuit?

Power is directly proportional to both voltage and current in a circuit. This means that as the voltage or current increases, the power also increases.

What are the units of power in a circuit?

The units of power in a circuit are watts (W). However, in some cases, kilowatts (kW) or milliwatts (mW) may also be used.

How does the power in a circuit affect the components?

The power in a circuit affects the components by determining how much energy they can handle. Components with higher power ratings can handle more energy and are therefore more durable. Additionally, the power in a circuit also affects the brightness of light bulbs and the speed of motors.

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