Question

Calculate the equivalent resistance b/w A and B of the above​

Answer 1

10 ohm is the required answer.

GIVEN:

• R1 = 6 ohm
• R2 = 4 ohm
• R3 = 8 ohm
• R4 = 8 ohm
• R5 = 5 ohm
• R6 = 6 ohm
• R7 = 2 ohm
• R8 = 6 ohm
• R9 = 3 ohm
• R10 = 4 ohm

TO FIND:

Net resistance, R across A and B.

FORMULAE:

• When the resistors are connected in series, net resistance, R = R1 + R2 + R3 + ......

• When the resistors are connected in parallel, then the net resistance, 1/R = 1/R1 + 1/R2 + 1/R3 + .....

SOLUTION:

1. R7 and R10 are in series. Let their effective resistance be Ra.

Ra = R7 + R10

= 2+4

Ra= 6 ohm

2. Ra and R8 are parallel. Let their effective resistance be Rb.

$\frac{1}{R_b} = \frac{1}{R_a} + \frac{1}{R_8} \\ \\ \frac{1}{R_b} = \frac{1}{6} + \frac{1}{6} \\ \\ \frac{1}{R_b} = \frac{2}{6} \\ \\ R_b = \frac{6}{2} \\ \\ R_b = 3 \: ohm$

3. Rb and R9 are in series. Let their effective resistance be Rc.

Rc = Rb + R9

= 3+ 3

Rc = 6 ohm

4. Rc and R6 are parallel. Let their effective resistance be Rd.

$\frac{1}{R_d} = \frac{1}{R_c} +\frac{1}{R_6} \\ \\ \frac{1}{R_d} = \frac{1}{6} + \frac{1}{6} \\ \\ \frac{1}{R_d} = \frac{2}{6} \\ \\ R_d = \frac{6}{2} \\ \\ R_d = 3 \: ohm$

5. Rd and R5 are in series. Let their effective resistance be Re.

Re = Rd + R5

= 3 + 5

Re = 8 ohm.

6. Re and R4 are parallel. Let their effective resistance be Rf.

$\frac{1}{R_f} = \frac{1}{R_e} +\frac{1}{R_4} \\ \\ \frac{1}{R_f} = \frac{1}{8} + \frac{1}{8} \\ \\ \frac{1}{R_f} = \frac{2}{8} \\ \\ R_f = \frac{8}{2} \\ \\ R_f = 4 \: ohm$

7.R2 and Rf are in series. Let their effective resistance be Rg.

Rg = R2 + Rf

= 4 + 4

Rg = 8 ohm

8.Rg and R3 are parallel. Let their effective resistance be Rh.

$\frac{1}{R_h} = \frac{1}{R_g} +\frac{1}{R_3} \\ \\ \frac{1}{R_h} = \frac{1}{8} + \frac{1}{8} \\ \\ \frac{1}{R_h} = \frac{2}{8} \\ \\ R_h = \frac{8}{2} \\ \\ R_h = 4 \: ohm$

9.Rh and R1 are in series. Let their effective resistance be R.

R = Rh + R1

= 4 + 6

R = 10 ohm

ANSWER:

The resistance across A and B is 10 ohm.

CIRCUIT DIAGRAM:

Refer to the attachment.