A stereo amplifier creates a 3.5 V potential difference across a speaker.

To double the power output of the speaker, the amplifier's potential difference must be increased to:

A. 7.0 V
B. 9.9 V
C. 12 V
D. 4.9 V

4.9

3.5*square root of 2

To solve this problem, we need to understand the relationship between power, voltage, and the speaker.

The power (P) in an electrical circuit can be calculated using the formula:

P = V^2 / R

where V is the voltage across the speaker and R is the resistance of the speaker.

Given that we want to double the power output, we can set up the following equation to solve for the new voltage (V2):

P2 = 2P1

(V2^2 / R) = 2(V1^2 / R)

We can simplify this equation by canceling out the resistance (R) on both sides:

V2^2 = 2V1^2

Now let's calculate:

V2^2 = 2(3.5 V)^2
V2^2 = 2(12.25 V^2)
V2^2 = 24.5 V^2

To solve for V2, we take the square root of both sides of the equation:

V2 = √(24.5 V^2)
V2 ≈ 4.95 V

Therefore, the potential difference across the speaker must be increased to approximately 4.95 V.

Among the answer choices provided, option D, 4.9 V, is the closest approximation to the correct answer.

Power is proportional to the square of voltage. What number is sqrt2 times 3.5 V ?