Question

In (Figure 1), R=15.0Ω and the battery emf is 6.30 V. Part A With switch S

2
​
open, switch S
1
​
is closed. After several minutes, S
1
​
is opened and S
2
​
is closed. At 2.40 ms after S
1
​
is opened, the current has decayed to 0.270 A. Calculate the inductance of the coil. Express your answer with the appropriate units. χ Incorrect; Try Again; 4 attempts remaining Part B How long after S
1
​
is opened will the current reach 1.00% of its original value? Express your answer with the appropriate units

Answer 1

To calculate the inductance of the coil, use the formula L = (R × t)/(ln(I0/I)). To find the time it takes for the current to reach 1.00% of its original value after S1 is opened, use the formula t = -Ln(0.01) × (L/R).

Step-by-step explanation:

The inductance of the coil can be calculated using the formula:

L = (R × t)/(ln(I0/I))

Where L is the inductance of the coil, R is the resistance in the circuit, t is the time, I0 is the initial current, and I is the current at the given time. Plug in the given values to calculate the inductance of the coil.

To calculate the time it takes for the current to reach 1.00% of its original value after S1 is opened, you can use the formula:

t = -Ln(0.01) × (L/R)

Where t is the time and Ln(0.01) is the natural logarithm of 0.01. Plug in the values of L and R to calculate the time.

Answer 2

The current to reach 1.00% of its original value after S1 is opened.

In this circuit, we can calculate the inductance (L) using the given values:

Given:

• R (resistance) = 15.0 Ω
• Initial current (I0) = not given (we'll use the final current after opening S1, which is 0.270 A)
• Current at time t (I) = 0 A (since S1 is opened)

The formula for inductance (L) is:

L = (R * t) / ln(I0 / I)

We'll use the values provided: R = 15.0 Ω, t = 2.40 ms (converted to seconds), I0 = initial current, and I = 0.270 A.

L = (15.0 Ω * (2.40 x 10^(-3) s)) / ln(I0 / 0.270 A)

You'll need to know the initial current (I0) to proceed with the calculation. If the initial current is not provided, you may need additional information or clarification.

Once you have the value of L, you can use it in Part B to calculate the time it takes for the current to reach 1.00% of its original value after S1 is opened. The formula for time (t) is:

t = -ln(0.01) * (L / R)

Substitute the values of L and R into the formula to find the time it takes for the current to reach 1.00% of its original value after S1 is opened.