Consider the combination of resistors shown in figure p 188...

Consider the combination of resistors shown in Figure $P 18.8$ . (a) Find the equivalent resistance between point $a$ and $b$ . (b) If a voltage of 35.0 $\mathrm{V}$ is applied between points $a$ and $b$ , find the current in each resistor.

Transcript

00:01 In this particular problem we need to find the equivalent resistance between a and b.

00:05 So let's start with step a and we are going to find equivalent resistance between 12 oms and 6 om and let us consider it as say r1 since these both resistances are in parallel we'll do the calculation as 12 into 6 upon 12 plus 6 which is coming as 4 oms.

00:42 So in this case the r1 value is of 4 oms.

00:47 In step b we'll try to find equivalent resistance between 4 oms and 8 oms.

01:06 Let us consider it as r2.

01:09 Since they are in parallel again we'll use the same formula 4 into 8 upon 4 plus 8 which is coming as 2 .67 oms so therefore we'll value of r2 is 2 .67 oms.

01:25 Now let's make a circuit here with the effective resistances that we have already calculated between a and b.

01:37 Now we'll denote it as r1, this r2 and the middle one is of 5 oms.

01:44 So value of r1 is 4 oms, value of r2 is 2 .67 oms.

01:52 Thus, total resistance, that is the effective resistance.

02:02 Between a and b is equal to let us take the notation as rt as 4 plus 5 plus 2 .67 which is coming as 11 .67 oms therefore effective resistance between a and b is of 11 .67 oms and this will be our first answer now in the next step we need to find current through each register.

02:45 So let's make a circuit first.

02:47 So here the circuit becomes, we need to connect these three resistances in the circuit with 35 volt battery attached as per the given statement.

03:08 So let me just write it as r1, r2, values are 4 -oom, 5 -oom, and 2 .6 -7 oms.

03:18 The current which is flowing to the circuit now is i.

03:25 So step a, the current through each register is equal to i, which is 35 volts divided by the combination of the resistances.

03:50 So 4 plus 5 plus 2 .67 oms and which is coming as 3 amperors.

04:00 So the current which is flowing to the circuit is of 3 ampiers.

04:08 Now in step b, we'll try to find the voltage across r1, 5 -oam and r2.

04:19 So let us write voltage across r1.

04:26 Take the notation as vr1, which is main current into r1.

04:33 So main current is of 3 -amperors, value of r1 is 4 -ooms...