Calculate the value of current in I₂. If R₁ = 10 ohms, R₂ =  20 ohms and I_s = 30A. 

Explanation:

Calculate the value of current in I2. If R1 = 10 ohms, R2 = 20 ohms and Is = 30A.

Given:

• R1 = 10 ohms
• R2 = 20 ohms
• Is = 30A

We need to find the current I2. Let's assume that R1 and R2 are in parallel connection and the source current Is is the total current supplied to the combination.

Solution:

In a parallel circuit, the voltage across each resistor is the same. Hence, we can write:

V = I1 * R1 = I2 * R2

Where,

• I1 is the current through resistor R1
• I2 is the current through resistor R2

Using Ohm's Law for parallel resistors, we have:

Is = I1 + I2

We know that:

I1 = V / R1

I2 = V / R2

Since the voltage across each resistor in parallel is the same, we can write:

V = I1 * R1 = I2 * R2

From this equation, we can express I1 in terms of I2:

I1 = (R2 / R1) * I2

Substitute this into the total current equation:

Is = (R2 / R1) * I2 + I2

Is = I2 * ((R2 / R1) + 1)

Now, solve for I2:

I2 = Is / ((R2 / R1) + 1)

Substitute the given values:

I2 = 30A / ((20 ohms / 10 ohms) + 1)

I2 = 30A / (2 + 1)

I2 = 30A / 3

I2 = 10A

Therefore, the value of current I2 is 10A.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 25A

This option is incorrect because the calculation does not support this value. If we substitute the values of the resistors and the total current into the formula, it does not give us 25A for I2.

Option 2: 15A

This option is incorrect as well. The correct calculation for I2, given the values of the resistors and the total current, does not result in 15A.

Option 4: 20A

This option is also incorrect. The calculated value for I2, using the given resistors and total current, does not equal 20A.

Conclusion:

When dealing with parallel circuits, it’s essential to remember that the voltage across each resistor is the same. Using Ohm’s Law and the formula for parallel resistors, we can accurately determine the current through each resistor. In this problem, we found that the correct value of current I2, considering the given resistances and total current, is 10A. This accuracy is crucial for ensuring the proper functioning and safety of electrical circuits.