Question

Как изменится период колебаний в электрическом контуре, если емкость конденсатора увеличится в 2 раза, а индуктивность катушки уменьшится в 4 раза?

Answer 1

Применяем формулу Томсона ,где  — индуктивность катушки,  — ёмкость конденсатора.отсюда получаем T=2пи*sqrt(1/4*2)=2*пи*sqrt(1/2)Ответ : увеличился sqrt(1/2) раза

Answer 2

Changes in the Period of Oscillation in an Electric Circuit

When the capacitance of a capacitor in an electric circuit increases by a factor of 2, and the inductance of a coil decreases by a factor of 4, the period of oscillation in the circuit will be affected.

The period of oscillation in an electric circuit is determined by the values of capacitance and inductance. The period is the time taken for one complete cycle of oscillation, usually measured in seconds.

According to the information provided, the capacitance of the capacitor increases by a factor of 2, while the inductance of the coil decreases by a factor of 4. To understand how these changes affect the period of oscillation, we can refer to the relevant physics principles.

The period of oscillation in an electric circuit can be calculated using the formula:

T = 2π√(LC)

Where: - T is the period of oscillation - π is a mathematical constant approximately equal to 3.14159 - L is the inductance of the coil - C is the capacitance of the capacitor

By substituting the given values into the formula, we can determine the changes in the period of oscillation.

Let's assume the initial values of capacitance and inductance are C1 and L1, respectively. After the changes, the new values are C2 and L2.

The period of oscillation with the initial values is given by:

T1 = 2π√(L1C1)

The period of oscillation with the new values is given by:

T2 = 2π√(L2C2)

To compare the changes, we can calculate the ratio of the new period to the initial period:

T2/T1 = (2π√(L2C2))/(2π√(L1C1))

Simplifying the equation:

T2/T1 = √(L2C2)/(√(L1C1))

Now, let's substitute the given changes into the equation:

- The capacitance of the capacitor increases by a factor of 2: C2 = 2C1 - The inductance of the coil decreases by a factor of 4: L2 = L1/4

Substituting these values into the equation:

T2/T1 = √((L1/4)(2C1))/(√(L1C1))

Simplifying further:

T2/T1 = √(2C1)/(2√(L1C1))

From this equation, we can see that the changes in capacitance and inductance affect the period of oscillation. However, without specific values for capacitance and inductance, we cannot determine the exact numerical change in the period.

To summarize, when the capacitance of a capacitor in an electric circuit increases by a factor of 2, and the inductance of a coil decreases by a factor of 4, the period of oscillation in the circuit will be affected. The exact change in the period can be calculated using the formula T2/T1 = √(2C1)/(2√(L1C1)), where C1 and L1 are the initial values of capacitance and inductance, respectively.

Please note that the specific numerical values of capacitance and inductance are not provided in the question, so we cannot determine the exact change in the period of oscillation.