Consider the following figure. (a) Find the equivalent resistance between points

Question

Consider the following figure.

(a) Find the equivalent resistance between points a and b in the figure. (R = 17.0 )


Incorrect: Your answer is incorrect.

Repeatedly apply, to one pair of resistors at a time, the rule for combining two resistors in parallel or two in series until you have reduced the entire combination of resistors into a single equivalent r.

(b) Calculate the current in each resistor if a potential difference of 54.0 V is applied between points a and b.
I (4.00 )   =      
A
I (7.00 )   =      
A
I (17.0 )   =      
A
I (9.00 )   =      
A

Explanation / Answer

Hi,

(a) The equivalent resistance of a group of resistances in series can be calculated as:

Req = R1 + R2 + .........

If the resistances are in parallel, the way to calculate it is:

1/Req = 1/R1 + 1/R2 + ........

Therefore:

As the resistances of 7 and 17 are in parallel, the equivalent resistance of them is:

1/R' = 1/7 + 1/17 = 0.202 ::::::::::: R' = 4.95

As the resistance of 4.95 , 4 and 9 are in series, the equivalent resistance of them is:

r = 4 + 9 + 4.95 = 17.95

(b) If we assume that Ohm's Law is in order, then we have the following:

I = V/R ; where V is the potential difference through the resistor and R is the value of the resistance.

The current through the points a and b can be calculated as:

I = Vt / r = 54 V / 17.95 = 3.0 A

Since the current is the same when the resistors are in series:

I = I(4.00 ) = I(9.00 ) = I(4.95 ) = 3.0 A

The current is splitted between the resistors in parallel and the potential difference remains the same, therefore:

Vr = I(4.95 )*R' = (3.0 A)(4.95 ) = 14.85 V

Then, the current in the resistors of 7 and 17 is:

I(7.00 ) = 14.85 V/7.00 = 2.12 A

I(17.00 ) = 14.85/17.00 = 0.87 A

I hope it helps.

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