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.