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.

202

likes
1012 views

Answer to a math 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.

Expert avatar
Jon
4.6
108 Answers
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}

where R_{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}

where V 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 becomes 2R_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)

Frequently asked questions (FAQs)
What is (2^3 * 3^2)^4 / (2^2 * 3^5)^2 ?
+
Find the square root of the sum of the first seven prime numbers.
+
What is the conversion of 45 degrees into radians?
+
New questions in Mathematics
a to the power of 2 minus 16 over a plus 4, what is the result?
12-6x=4x+2
3(2+x)-2(2x+6)=20-4x
What payment 7 months from now would be equivalent in value to a $3,300 payment due 23 months from now? The value of money is 2.7% simple interest. Round your answer to 2 decimal places. Show all work and how you arrive at the answer..
A client did not advance L 10,000 for the rental of a parking area and it corresponds to 4 months, of which 2 months were consumed
Elliot opened a savings account and deposited $5000.00 as principal. The account earns 4% interest, compounded annually. How much interest will he earn after 5 years? Round your answer to the nearest cent.
Moaz wanted to test whether the level of headache pain (on a scale of 1 – 10) changes after taking Advil. He collected data from 9 participants and calculated the difference in headache pain before and after taking Advil (summarized in the table below). Determine W observed for this test. Difference Scores -2 -4 0 +1 +3 -2 0 -3 -5 Also, What is the degrees of freedom for this test?
find all matrices that commute with the matrix A=[0 1]
Suppose that you use 4.29 g of Iron in the chemical reaction: 2Fe(s) + 3 Cu2 + (aq) 2Fe 3 + (aq) + 3Cu(s ) - . What is the theoretical yield of Cu (s), in grams?
Shows two blocks, masses 4.3 kg and 5.4 kg, being pushed across a frictionless surface by a 22.5-N horizontal force applied to the 4.3-kg block. A. What is the acceleration of the blocks? B. What is the force of the 4.3-kg block on the 5.4 -kg block? C. What is the force of the 5.4 -kg block on the 4.3 -kg block?
1. A capital of $3,831 was lent, and it has produced interest of $840 from 05-12-2022 to 1-12-2023. At what annual simple interest rate was the capital lent?
Sabendo+que+o+tri%C3%A2ngulo+ABC+%C3%A9+ret%C3%A2ngulo+e+que+um+de+seus+%C3%A2ngulos+mede+30+quanto+mede+o+terceiro+ tri%C3%A2ngulo
(X+2)(x+3)=4x+18
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
Solve for B write your answer as a fraction or as a whole number. B-1/7=4
A property sold for $745,000 in a co-brokered transaction. The seller has agreed to pay a 7% commission to the listing firm. The listing firm has agreed to equally split the commission with the selling firm. If the buyer’s broker will receive 8% of the selling firm’s commission, how much commission will the buyer’s broker receive? $14,900 $3725 $$37250 $18625
What is the percentage of nitrogen abundance in copper dinatrate Cu(NO3)2
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
Sally’s sales for last Sunday were $1,278. That was an increase of 6.5% over her sales for the previous Saturday. What were her sales for the previous Saturday?
t+72/t=-17