Question

Find the equivalent resistance of the following circuit.​

Answer 1

16.045 ohm is the required answer.

GIVEN:

$R_1$ = 10 ohm

$R_2$ = 5 ohm

$R_3$ = 25 ohm

$R_4$ = 5 ohm

$R_5$ = 5 ohm

$R_6$ = 20 ohm

TO FIND:

Equivalent resistance, R

FORMULA:

• When resistors are in series, R = $R_1 + R_2 + R_3$...

• When resistors are in parallel, $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} .....$

SOLUTION:

STEP 1:

$R_1$ and $R_2$ are in series. Let their effective resistance be $R_x$.

$R_x = R_1 + R_2$

= 10 + 5

$R_x$ = 15 ohm

STEP 2:

$R_4$ and $R_5$ are in series. Let their effective resistance be $R_y$

$R_y$ = $R_4$ + $R_5$

= 5 + 5

$R_y$ = 10 ohm

STEP 3:

$R_x$ and $R_3$ are parallel. Let their effective resistance be $R_a$.

$\frac{1}{R_a} = \frac{1}{R_x} + \frac{1}{R_3} \\ \\ = \frac{1}{15} + \frac{1}{25} \\ \\ = \frac{25 + 15}{15 \times 25} \\ \\ \frac{1}{R_a} = \frac{40}{375} \\ \\ R_a = \frac{375}{40} \\ \\ R_a = 9.375 \: ohm$

STEP 4:

$R_y$ and $R_6$ are in parallel. Let their effective resistance be $R_b$.

$\frac{1}{R_b} = \frac{1}{R_y} + \frac{1}{R_6} \\ \\ = \frac{1}{10} + \frac{1}{20} \\ \\ = \frac{20 + 10}{20 \times 10} \\ \\ = \frac{30}{200} \\ \\ R_b = \frac{200}{30} \\ \\ R_b = 6.67 \: ohm$

STEP 5:

$R_a$ and $R_b$ are in series. Let their effective resistance be R.

R = $R_a$ + $R_b$

= 9.375 + 6.67

R = 16.045 ohm

ANSWER:

The effective resistance is 16.045 ohm.