Suppose the resistor $R_{1}$ , $R_{2}$ , and $R_{3}$ have the value $5 Ω, 10 Ω$ and $30 Ω$ respectively .Which have been connected to a battery of $12 V$ in parallel connection.Calculate.
(i) The current through each resistor.
(ii) The total current in the circuit.
(iii) The total circuit resistance.

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Solution

The equivalent resistance of the 5Ω, 10Ω, 30Ω resistors connected in parallel is
$\frac{1}{R_{p}} = \frac{1}{5} + \frac{1}{10} + \frac{1}{30}$
$= \frac{6 + 3 + 1}{30} = \frac{10}{30}$
$∴ R_{p} = 3 Ω$
$∴$ , the total resistance of the given circuit is $3$ Ohms.
The total current can be calculated using the Ohm's law as the value of voltage $(V)$ is already given.
using Ohm's law
Voltage $=$ Current $\times$ Resistance
$\Rightarrow I = \frac{V}{R} = \frac{12}{3} = 4$ A
Current through each resistor can be calculated by applying Ohm's law given that the voltage of the circuit and the individual resistances of each resistor is already given.
Current through $5 Ω$ resistor $= \frac{V}{R} = \frac{12}{5} = 2.4$ A
Current through $10 Ω$ resistor $= \frac{V}{R} = \frac{12}{10} = 1.2$ A
Current through $30 Ω$ resistor $= \frac{V}{R} = \frac{12}{30} = 0.4$ A

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Suppose the resistor R1 , R2 , and R3 have the value 5Ω,10Ω and 30Ω respectively .Which have been connected to a battery of 12 V in parallel connection.Calculate.(i) The current through each resistor.(ii) The total current in the circuit.(iii) The total circuit resistance.