#1 If the inductance in the LC circuit is quadrupled the natural frequency of that circuit will

a)increase to 4 times its original value
b)increase to twice its original value
c)decrease to 1/2 of its original value
d)decrease to 1/4 of its original value

Isn't the correct choice c) since f=1/2pisqrt(LC)?

#2 If the capacitance in the LC circuit is reduced by a factor of four the natural frequency of that circuit will
a)increase to 4 times its original value
b)increase to twice its original value
c)decrease to 1/2 of its original value
d)decrease to 1/4 of its original value

Isn't the correct choice b) since f=1/2pisqrt(LC)?

yes

In order to determine the effect of changing the inductance or capacitance on the natural frequency of an LC circuit, you are correct in using the formula f = 1 / (2π√(LC)). Let's go through each question to find the correct answers.

#1 If the inductance in the LC circuit is quadrupled, the natural frequency of that circuit will:

To find the new natural frequency, we need to consider how changing the inductance affects the formula. Since we are quadrupling the inductance, we can substitute 4L for L in the formula:

f = 1 / (2π√(4L*C))

We can simplify this expression to:

f = 1 / (2π * 2√(LC))

f = 1 / (4π√(LC))

From this expression, we can see that the natural frequency is decreased by a factor of 4. Therefore, the correct answer is d) decrease to 1/4 of its original value.

#2 If the capacitance in the LC circuit is reduced by a factor of four, the natural frequency of that circuit will:

Again, we need to substitute the new value into the formula:

f = 1 / (2π√(L*(C/4)))

Simplifying this expression gives us:

f = 1 / (2π * √(L*C/4))

f = 1 / (2π * (√(L*C) / √(4)))

f = 1 / (2π * (√(L*C) / 2))

We can cancel out the 2s:

f = 1 / (π√(L*C))

From this expression, we can see that the natural frequency is increased by a factor of 2. Therefore, the correct answer is a) increase to 4 times its original value.

In both cases, the correct answers are different from the options you suggested. So, for question #1, the correct answer is d) decrease to 1/4 of its original value, and for question #2, the correct answer is a) increase to 4 times its original value.