In periods of peak demand, power companies lower their voltage. This saves them power (and saves you money!). To see the effect, consider a 1200- W coffeemaker that draws 10 A when connected to 120 V. Suppose the voltage is lowered by 13 % to 104 V.(Caution: The 1200- W label is valid only when 120 V is applied. When the voltage is lowered, it is the resistance of the toaster, not its power, that remains constant.)
1)By how much does the current decrease?
2)By how much does the power decrease?
R = 120V / 10A = 12 Ohms.
1. I = V/R = 104 / 12 = 8.67 Amps.
Change = 10 - 8.67 = 1.33 Amps.
2. P = VI = 104 * 8.67 = 902 Watts.
Change = 1200 - 902 = 298 Watts.
1) Well, when the voltage decreases, it's like the power company is trying to give your coffee maker a little chill pill. So, if we have a decrease of 13% in voltage, we can expect the current to decrease as well. How much? Let's find out!
The original voltage is 120 V and the decreased voltage is 104 V. To find the decrease in current, we can use Ohm's Law: V = IR.
At 120 V, the coffee maker draws 10 A. So, 120 = I * 10. Solving for I, we get I = 12 A.
Now, since the resistance of the coffee maker remains constant, we can use the new voltage (104 V) and the original resistance to find the new current. Let's plug those values into Ohm's Law: 104 = I2 * 10. Solving for I2, we get I2 = 10.4 A.
So, the current decreases by approximately 1.6 A (12 A - 10.4 A).
2) Now, let's talk about the power decrease. If I were a power company, I'd definitely be afraid of coffee makers running wild all over the place. So, let's see how the power changes when the voltage decreases.
The original power is 1200 W when the coffee maker is connected to 120 V. Now, with the decreased voltage of 104 V, we can use the formula: P = IV to find the new power.
So, the original power is 1200 = 10 * 120. Solving for I, we get I = 12 A.
Using the new voltage (104 V) and the new current (10.4 A), we can find the new power. Plugging those values into the formula: P = 10.4 * 104, we get P ≈ 1081.6 W.
Therefore, the power decreases by approximately 118.4 W (1200 W - 1081.6 W). That's like taking a sip out of your coffee maker's power!
So, there you have it - the current decrease is around 1.6 A and the power decrease is about 118.4 W. The power company is just trying to keep your coffee maker in check. They don't want it to get too hyper!
To determine the answers, we need to calculate the new current and power values after the voltage is lowered.
1) By how much does the current decrease?
The current can be calculated using Ohm's Law formula: I = V/R, where I is the current, V is the voltage, and R is the resistance.
Given:
Initial voltage (V1) = 120 V
Lowered voltage (V2) = 104 V
Resistance (R) remains constant.
We can set up the following equation:
I1 = V1 / R
I2 = V2 / R
Substituting the given values:
I1 = 120 V / R
I2 = 104 V / R
To find the decrease in current, we can calculate the difference:
Decrease in current = I1 - I2 = (120 V / R) - (104 V / R)
2) By how much does the power decrease?
The power can be calculated using the formula: P = VI, where P is the power, V is the voltage, and I is the current.
Given:
Initial power (P1) = 1200 W
Initial current (I1) = 10 A
Lowered voltage (V2) = 104 V
We can set up the following equation:
P1 = V1 * I1
P2 = V2 * I2
Substituting the given values:
P1 = 120 V * 10 A
P2 = 104 V * I2
To find the decrease in power, we can calculate the difference:
Decrease in power = P1 - P2 = (120 V * 10 A) - (104 V * I2)
Please note that further calculations depend on the precise value of the resistance (R).
To answer these questions, we need to apply the concept of Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance.
Let's start by finding the resistance of the coffee maker. We can use the power equation, P = V * I, rearranged to solve for resistance (R = V / I).
1) Calculate the resistance:
Given voltage, V = 120 V
Given current, I = 10 A
Resistance, R = V / I = 120 V / 10 A = 12 Ω
Now let's consider the effect of lowering the voltage by 13% to 104 V.
2) Calculate the new current:
Given new voltage, V' = 104 V
Using Ohm's Law (V' = I' * R), we can rearrange it to solve for the new current (I'):
I' = V' / R = 104 V / 12 Ω = 8.67 A (rounded to two decimal places)
1) The current decreases by approximately 1.33 A.
Now, let's find the effect on the power.
2) Calculate the new power:
Using the equation P = V * I and the new current calculated above, we can find the new power (P'):
P' = V' * I' = 104 V * 8.67 A = 901.68 W (rounded to two decimal places)
2) The power decreases to approximately 901.68 W.
By lowering the voltage, the current and power consumed by the coffee maker decrease.