Solve Current Divider Rule for Resistor Currents w/ R & i

  • Thread starter Thread starter jti3066
  • Start date Start date
  • Tags Tags
    Current
AI Thread Summary
The discussion focuses on applying the current divider rule (CDR) to find the current through three resistors connected in parallel, specifically with resistances of 4 ohms, 2 ohms, and an unknown resistor R. The poster initially struggles with the correct application of the CDR formula, questioning their derived expressions for the currents through each resistor. They express confusion about the correct formulation, particularly in how to incorporate the total resistance and the individual resistances into the calculations. The conversation emphasizes the importance of understanding the voltage across the parallel resistors to accurately calculate the current through each one. Ultimately, the discussion seeks clarity on the effective resistance of the parallel combination and the resulting current values.
jti3066
Messages
46
Reaction score
0

Homework Statement



Three resistors with resistance 4 ohms, 2 ohms, and R are connected in parallel. There is a total current i through the network. Find the current through each resistor in terms of R and i.

Ignore the 4 ohms and 2 ohms for now I just need help with the CDR formula...Thanks

Homework Equations



i_0 = i_1 + i_2 + i_3

V = V_1 + V_2 + V_3

V_n = i_n * R_n


The Attempt at a Solution



Following the current divider rule I came to the "answer":

i_n = i_0(R_total/R_n)

so for example

i_1 = i_0((R_1 + R_2 + R_3)/R_1)

However my example problem states that the answer should be:

i_1 = i_0(R_2/(R_1 + R_2 + R_3))...?
 
Physics news on Phys.org
Wait...is this correct?

i_1 = i_0(R_2 + R_3/R_total)

i_2 = i_0(R_3/R_total)

i_3 = i_0(0/R_total) = 0 because there are no resistor to the right of R_3
 
What's the effective resistance of the parallel combination of three resistors? Call them R1, R2, R3.

Since the total current through the parallel group given as i, what's the voltage across all three? And, given the voltage across all three, you are now in a position to calculate the current though each, right?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Finding the current and voltage for a resistor
Replies
16
Views
2K
Is This a Series or Parallel Circuit?
Replies
13
Views
899
Using Kirchoff's Loop Rule to Determine Currents in a Circuit
Replies
2
Views
2K
Analyzing Bridge Circuit w/ Loop Currents
Replies
6
Views
1K
Complex RLC Circuit Problem (System of diff eqs)
Replies
6
Views
2K
A circuit with multiple sources of voltage
Replies
2
Views
1K
Finding the Current in a circuit
Replies
6
Views
3K
Finding the resistance in a parallel-series circuit.
Replies
17
Views
2K
Finding Voltages Using KVL & KCL
Replies
1
Views
1K
Determine the magnitudes and directions of the currents in each R's.
Replies
2
Views
9K

Hot Threads

Recent Insights

Back
Top