A constant voltage is applied across a circuit. If the resistance in the circuit is doubled, what is the effect on the power dissipated by the circuit?
a. The power dissipated is reduced by a factor of 4.
b. The power dissipated is quadrupled.
c. The power dissipated is doubled.
d. The power dissipated is reduced by a factor of 2.
e. The power dissipated remains constant.
d. Reduced by a factor of 2: P = V^2/2R.
The power dissipated by a circuit can be calculated using the formula P = V^2/R, where P is power, V is voltage, and R is resistance.
If the resistance in the circuit is doubled while the voltage remains constant, we can substitute 2R for R in the power formula:
P' = V^2/(2R)
To simplify this expression, we can divide the denominator by 2:
P' = V^2/R * (1/2)
Therefore, when the resistance is doubled, the power dissipated by the circuit is reduced by a factor of 2.
So, the correct answer is option d. The power dissipated is reduced by a factor of 2.
To determine the effect of doubling the resistance in a circuit on the power dissipated, you need to understand the relationship between power, voltage, and resistance.
The formula for calculating power in an electrical circuit is given by P = V^2 / R, where P represents power, V represents voltage, and R represents resistance.
In this case, we have a constant voltage applied across the circuit. Since the voltage remains constant, the power dissipated in the circuit is inversely proportional to the resistance. This means that as the resistance increases, the power dissipated decreases.
So, if the resistance is doubled, the power dissipated will be reduced.
Now let's analyze the answer options:
a. The power dissipated is reduced by a factor of 4. - This answer is incorrect because doubling the resistance reduces the power, but it is not reduced by a factor of 4.
b. The power dissipated is quadrupled. - This answer is also incorrect. Doubling the resistance reduces the power dissipated, not quadruples it.
c. The power dissipated is doubled. - This answer is incorrect. Doubling the resistance reduces the power dissipated, so it is not doubled.
d. The power dissipated is reduced by a factor of 2. - This answer is correct. Doubling the resistance reduces the power dissipated by a factor of 2.
e. The power dissipated remains constant. - This answer is incorrect. As explained earlier, doubling the resistance decreases the power dissipated.
Therefore, the correct answer is d. The power dissipated is reduced by a factor of 2.