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
86 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 the unit vector in the direction of V = (2, -3, 4)?
+
Find the derivative of the function g(x) = ∫[a, x] f(t) dt.
+
Find the basis vectors for a plane in R^3 defined by the equation 2x + 3y - z = 0.
+
New questions in Mathematics
Find two natural numbers whose sum is 230 and their difference is 10. Set up the system and solve it.
2+2
90 divided by 40
Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.
The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randomly selected, what is the probability that the sample mean would be less than 121 months? Round your answer to four decimal places
Convert 78 percent to a decimal
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.
TEST 123123+1236ttttt
cube root of 56
Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)
find missing measure for triangle area = 48 m square base = 10m heaighy = ? m
Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?
Below are three 95% CIs (where 𝜎 was known and 𝑥̅happened to be the same); one with sample size 30, one with samplesize 40, and one with sample size 50. Which is which?(66.2, 76.2)(61.2, 81.2)(56.2, 86.2)
Evaluate ab+dc if a=56 , b=−34 , c=0.4 , and d=12 . Write in simplest form.
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
2.3 X 0.8
6(k-7) -2=5
Sarah is lining a square tray with 1 inch square tiles. the side length of the tray is 9 inches. How many tiles does Sarah need?
Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.