resistors A,B and C are connected in a parallel wth one another?

Question

if A&B have the same resistance & C has 1/2 of either A or B's resistance,find the current of each resistors if ,the current taken from the supply is 8 amperes

Answer 1

a and b will have the same current. C will have 2x the current of a or b since they all have the same voltage connected and I=V/R so 1/2 the resistance is 2x the current.

So, if the current through A and B is X, and total current is 8:

X+X+2X = 8
4X= 8
X = 2

2 amps through A
2 amps through B
4 amps through C

Answer 2

Here's the hard way:

1) Find the equivalent resistance of A || B || C, which is the same as the equivalent resistance of A || A || A/2.

2) The answer to 1 is the total resistance. Since V = IR and I = 8 amps, you can now figure out V.

3) Use V / R = I to find the current in each resistor.


Here's the easy way -- translate the problem into something equivalent but easier to think about:

How do you divide 8 amps through the 3 resistors so that the voltage across each resistor is the same?

You know that Resistor C carries twice the current that A carries, and A and B carry the same amount of current, since they have the same resistance. Thus, if Ia = the current in Resistor A, then the total current is Ia + Ia + 2Ia = 4Ia = 8.
8 / 4 = 2 amps = Ia.

Answer 3

For parallel circuits, resistance is added by:

1/Total Resistance= 1/R+1/R+2/R, where 1/R describes the resistances in A and B, and 2/R in C.

Adding A and B gives 2/R, which is equal to C. What this means is that the current will face an equal resistance in A and B together as it does in C. If you imagine that current is like a waterflow, it flows at greatest speed where resistance is lowest. But 1/2 of that current is divided equally between A and B, and the rest goes to C. So 1/2 of 8 amps goes to C, or 4 amps, and 2 amps each to A and B.