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 = 18.0 ?)
  ?

(b) Calculate the current in each resistor if a potential difference of 22.0 V is applied between points a and b.

I (4.00 ?) =     A I (7.00 ?) =     
I (18.0 ?) =     
.A I (9.00 ?) =     A Consider the following figure. (a) Find the equivalent resistance between points a and b in the figure. (R = 18.0 ?) ? (b) Calculate the current in each resistor if a potential difference of 22.0 V is applied between points a and b. I (4.00 ?) = A I (7.00 ?) = I (18.0 ?) = .A I (9.00 ?) = A

Explanation / Answer

For this first we need to resolve the Parallel part of the wire. So, the formula will be-

1/R' = 1/7 + 1/R= 1/7 + 1/18= 18+7/18*7= 25/126 R' = 126/25= 5.04 ohm

Now we will consider this as a Series Combination and the formula is-

R'' = 4+ 5.04+ 9 = 18.04 ohm

Now, current remains same in series, But first we need to find the total current using the formula-

V= IR 22= I* [18.04] I = 22/18.04 = 1.2 A

Now 1.2 A is same through resistors connected in series. Therefore, I [4 ohm] = I [9 ohm] = 1.2 A

Before finding current through the parallel connection we need to find the Potential difference between c and d. Total resistance across c and d is 5.04 ohm, and current is 1.2 A. So, Potential difference will be

V= IR= 1.2* 5.04= 6.04 V

This will be same for both the resistors in Parallel connection- 7 ohm & 18 ohm.

I [7 ohm] = V/R = 6.04/7= 0.864 A I [18 ohm]= 6.04/18= 0.336

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