Find the expression for Power in circuit

VitaminK · Mar 10, 2020

I was wondering if someone could check my answer and see if it is correct.
The resistance in series is Req= R+ R= 2R

Circuit schematic of a battery labelled V in series with two lamp-style resistors labelled R1 and R2, with voltmeter-style labels V1 and V2 placed across each resistor.

Circuit schematic of a battery in series with a single lamp symbol and a resistor labelled 2R, all connected in one closed loop.

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

Handwritten equation: P = V^2 / R_eq → P = V^2 / 2R, with a right arrow between the two expressions.

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

Equation V = R × I → I = V1/R1, with V = R × I written on the left and an arrow leading to I = V1 over R1 on the right.

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

$Equation: P = I^2 × Req = (V1/R1)^2 × 2R = V1^2 × 2 / R, with fractions and exponents as shown.$

However i don't get the same answer :(

Merlin3189 · Mar 10, 2020

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.

Find the expression for Power in circuit

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