Question

If a two-branch parallel current divider network, if the resistance of one branch is doubled while keeping all other factors constant, what happens to the current flow through that branch and the other branch? Select one: a. The current through the doubled resistance branch remains unchanged, and the current through the other branch decreases. b. The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged. c. The current through the doubled resistance branch increases, and the current through the other branch remains unchanged. d. The current through both branches remain unchanged.

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To determine what happens to the current flow through the branches in a two-branch parallel current divider network when the resistance of one branch is doubled, we can use the current divider rule.

The current divider rule states that the current through a particular branch in a parallel network is inversely proportional to the resistance of that branch compared to the total resistance of the network.

Let's assume that the resistance of the first branch is increased by a factor of 2 while the resistance of the second branch remains the same.

Step 1: Calculate the equivalent resistance of the network

The equivalent resistance of a parallel network can be calculated using the formula:

\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}

whereR_{eq} is the equivalent resistance, R_1 is the resistance of the first branch, and R_2 is the resistance of the second branch.

Since the resistance of the second branch remains unchanged, we can write:

\frac{1}{R_{eq}} = \frac{1}{(2R_1)} + \frac{1}{R_2}

Simplifying, we get:

\frac{1}{R_{eq}} = \frac{3}{2R_1}

Therefore, the equivalent resistance,R_{eq} , is:

R_{eq} = \frac{2R_1}{3}

Step 2: Calculate the current through each branch

Using the current divider rule, the current through the first branch can be calculated as:

I_1 = \frac{V}{R_1}

whereV is the voltage across the parallel network.

Similarly, the current through the second branch is:

I_2 = \frac{V}{R_2}

Step 3: Calculate the new currents after doubling the resistance of the first branch

After doubling the resistance of the first branch, the new resistance becomes2R_1 .

Using the current divider rule, the new current through the first branch,I_1' , can be calculated as:

I_1' = \frac{V}{2R_1}

The current through the second branch,I_2' , remains the same:

I_2' = \frac{V}{R_2}

Answer: The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged. (Option b)

The current divider rule states that the current through a particular branch in a parallel network is inversely proportional to the resistance of that branch compared to the total resistance of the network.

Let's assume that the resistance of the first branch is increased by a factor of 2 while the resistance of the second branch remains the same.

Step 1: Calculate the equivalent resistance of the network

The equivalent resistance of a parallel network can be calculated using the formula:

where

Since the resistance of the second branch remains unchanged, we can write:

Simplifying, we get:

Therefore, the equivalent resistance,

Step 2: Calculate the current through each branch

Using the current divider rule, the current through the first branch can be calculated as:

where

Similarly, the current through the second branch is:

Step 3: Calculate the new currents after doubling the resistance of the first branch

After doubling the resistance of the first branch, the new resistance becomes

Using the current divider rule, the new current through the first branch,

The current through the second branch,

Answer: The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged. (Option b)

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