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Electricity — Science STD 10 — Question

Maharashtra 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 $AB = IR_3 = 1 \times 5 = 5V$
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 $AC = IR = 1 \times 11 = 11V$
  1. Total resistance $= R_3 + R' = 5 + 6 = 11$ ohm.

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