Question

In the following figure calculate:

1. the total resistance of the circuit
2. the value of R, and
3. the current flowing in R.

Answer 1

(a) V = 4 V; I = 0.4 A

Total Resistance R'=?

R' = ${\displaystyle \frac{\text{V}}{\text{I}}=\frac{4}{0.4}}$ = 10 Ω

(b) R₁ = 20 Ω; R' = 10 Ω

${\displaystyle \frac{1}{\text{R'}}=\frac{1}{\text{R}}+\frac{1}{{\text{R}}_1}}$

${\displaystyle \frac{1}{10}=\frac{1}{\text{R}}+\frac{1}{20}}$

${\displaystyle \frac{1}{\text{R}}=\frac{1}{10}-\frac{1}{20}}$

${\displaystyle \frac{1}{\text{R}}=\frac{2-1}{20}}$

${\displaystyle \frac{1}{\text{R}}=\frac{1}{20}}$

R = 20 Ω

(c) R = 20 ohm; V = 4 V

I = ${\displaystyle \frac{\text{V}}{\text{R}}=\frac{4}{20}}$ = 0.2 A