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Electricity — Science STD 10 — Question

CBSE BoardEnglish MediumSTD 10ScienceElectricity5 Marks
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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