With the help of a circuit diagram, obtain the relation for the equivalent resistance of two resistances connected in parallel. In the circuit diagram shown below, find:
- Total resistance.
- Current shown by the ammeter $A$
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- Suppose total current flowing the circuit is I then the current passing through resistance $R_1 $ will be $I_1$ and current passing through resistance $R_2$ will be $I_2$
Let resultant resistance of this parallel combination is R. By applying the ohm's law to each resistance we get that,
$\text{I}_1=\frac{\text{V}}{\text{R}_1}$
$\text{I}_2=\frac{\text{V}}{\text{R}_2}$
putting these eq in the above one, we get that
$\frac{\text{V}}{\text{R}}=\frac{\text{V}}{\text{R}_1}+\frac{\text{V}}{\text{R}_2}$
$\frac{1}{\text{R}}=\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}$
If two resistance are connected in parallel than the resultant resistance will be
$\frac{1}{\text{R}}=\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}$
- Total resistance $= R$
$R_2 = 3 + 2 = 5$ ohms
$R_1 = 5$ ohm
$\frac{1}{\text{R}}=\frac{1}{5}+\frac{1}{5}$
$\frac{1}{\text{R}}=\frac{2}{5}$
$R = 2.5$ ohm
Current flows through the circuit
$\text{I}=\frac{\text{V}}{\text{R}}=\frac{4}{2.5}$
$= 1.6$ amps
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