Question
Three resistors are connected as shown in the diagram.

Through the resistor 5 ohm, a current of 1 ampere is flowing,
  1. What is the current through the other two resistors?
  2. What is the p.d. across AB and across AC?
  3. What is the total resistance?

Answer


According to the diagram
  1. Total current I = 1 amp is entering the parallel combination of R1 and R. Let I1 current flows through R1 and I2 current flows through R2
Then

$\text{I}_1=\frac{\text{IR}_2}{\text{R}_1+\text{R}_2}$

$=\frac{1\times15}{10+15}=0.6\text{A}$

$\text{I}_2=\frac{\text{IR}_2}{\text{R}_1+\text{R}_2}$

$=\frac{1\times10}{10+15}=0.4\text{A}$
  1. p.d. across AB = $IR_3 = 1 × 5 = 5V$
Equivalent resisyance between B and C is

$\frac{1}{\text{R}'}=\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}=\frac{1}{10}+\frac{1}{15}$

$\frac{1}{\text{R}'}=\frac{5}{30}$

R' = 6 ohm

Total resistance between A and C is R = 5 + 6 = 11 ohm

p.d. across AC = IR = 1 × 11 = 11V
  1. Total resistance $=R_3+R^{\prime}=5+6=11$ ohm.

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