In a certain stereo system, each speaker has a resistance of 4 Ω. The system is rated at 60 W in each channel. Each speaker circuit includes a fuse rated at a maximum current of 4 A. Is this system adequately protected against overload?
Did you forget to square root 15? Because I^2 = 15, so I = sqrt 15 = 3.87. If that is the answer, then the speaker IS adequately protected.
To determine if the stereo system is adequately protected against overload, we need to compare the maximum current rating of the fuse to the current drawn by the system.
First, let's find the current drawn by the system. We can use Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R).
Given:
Resistance of each speaker (R) = 4 Ω
Power rating of each channel (P) = 60 W
We can use the formula:
P = V^2 / R
Rearranging the formula to solve for voltage (V):
V = sqrt(P * R)
Let's calculate the voltage:
V = sqrt(60 * 4)
V = sqrt(240)
V ≈ 15.49 V
Now, to find the current drawn by the system, let's divide the voltage by the resistance:
I = V / R
I = 15.49 V / 4 Ω
I ≈ 3.87 A
Since the current drawn by the system is approximately 3.87 A, which is less than the maximum current rating of the fuse (4 A), we can conclude that the system is adequately protected against overload.
To determine if the stereo system is adequately protected against overload, we need to compare the maximum current rating of the fuse with the current that would flow through the circuit at maximum power.
First, let's calculate the current flowing through each channel using the power and resistance values provided. We can use Ohm's Law, which states that current (I) is equal to power (P) divided by resistance (R), or I = P / R.
For each channel:
Power (P) = 60 W
Resistance (R) = 4 Ω
I = P / R
I = 60 W / 4 Ω
I = 15 A
Therefore, the current flowing through each speaker circuit at maximum power is 15 A, which exceeds the maximum current rating of the fuse (4 A).
Since the maximum current that can pass through the speaker circuit exceeds the maximum current rating of the fuse, the system is not adequately protected against overload. In the event of an overload, the fuse would likely blow, interrupting the circuit and potentially protecting the system from damage.
To ensure adequate protection, you would need to use a fuse with a higher current rating that can handle the maximum current of 15 A.
What current would flow in the speaker if it were using 60W?
P = I^2*R
I^2 = P/R 60/4 = 15 A
Imax would be less than 4 Amps.
If the fuse does not blow until current reaches 4A, the speaker is NOT adequately protected.