Question

In the circuit diagram suppose the resistors R1, R2 and R3 have the values of 5Ω, 10Ω and 30Ω respectively which have been connected to a 12V battery in parallel.Calculate (a) current through each resistor (b) the total current in the circuit (c) the total circuit resistance.

Answer 1

Answer:

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Answer 2

Answer: (a) Current through each resister 5 Ohm, 10 Ohm and 30 Ohm are 2.4A, 1.2A and 0.4A.

(b) The total current in the circuit is 4A.

(c) The total resistance is 3 Ohm.

Explanation:

Given that:

 • The equivalent resistance of the 5Ω, 10Ω, 30Ω resistors connected in parallel to a 12V battery.

So, $v= 12V$.

1. Finding the resultant resistance:

We know that:

 •  $\frac{1}{R_{P} }=\frac{1}{5}+\frac{1}{10}+\frac{1}{30}=\frac{6+3+1}{30} =3$

    $R_{P}=3$

Where, $R_{P}$  is the resultant resistance.

Therefore, the total resistance of the given circuit is 3 Ohms.

2. Finding the total current in the circuit:

The total current can be calculated as follows:

Using Ohm's law, we know;

Voltage = Current * Resistance

$I=\frac{V}{R}=\frac{12}{3}=4A$

$I=4A$

So, the total current in the circuit is 4A.

3. Current through each resister:

Using the same Ohm’s law we can find the current through each resister.

Given that the voltage of the circuit is 12V and the individual resistances of each resistor is already given in the question.

Current through 5Ω resistor, $\frac{V}{R}=\frac{12}{5}=2.4A$

Current through 10Ω resistor, $\frac{V}{R}=\frac{12}{10}=1.2A$

Current through 30Ω resistor, $\frac{V}{R}=\frac{12}{30}=0.4A$

Current through through each resistance is 2.4A, 1.2A and 0.4A respectively.