Resistors $R_{1}$ , $R_{2}$ and $R_{3}$ having values 5 $Ω$ , 10 $Ω$ , and 30 $Ω$ respectively are connected in parallel across a battery of 12V. Calculate [3 MARKS]

(a) the current through each resistor

(b) the total current in the circuit and

(c) the total circuit resistance.

Open in App

Solution

Each point: 1 Mark

Here,
$R_{1} = 5 Ω, R_{2} = 10 Ω, R_{3} = 30 Ω, V = 12 V$
(a) $I_{1} = ?$ $I_{2} = ?$ $I_{3} = ?$

(b) $I = I_{1} + I_{2} + I_{3} = ?$

(c) $R_{p} = ?$

(a) From relation, (Ohm's law), $R = \frac{V}{I}$

$I = \frac{V}{R}$

Putting values, we get, $I_{1} = \frac{V}{R_{1}} = \frac{12}{5} = 2.4 A$

$I_{2} = \frac{V}{R_{2}} = \frac{12}{10} = 1.2 A$

$I_{3} = \frac{V}{R_{3}} = \frac{12}{30} = 0.4 A$

(b) Total current, $I = I_{1} + I_{2} + I_{3}$

$I = 2.4 + 1.2 + 0.4 = 4 A$

(c) From relation
$\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$

$R_{p} = 3 Ω$

Suggest Corrections

Similar questions

R_{1}

R_{2}

R_{3}

5 Ω, 10 Ω, 30 Ω

Resistors $R_{1}$ =10 $Ω$ , $R_{2}$ = 40 $Ω$ , $R_{3}$ = 30 $Ω$ , $R_{4}$ = 20 $Ω$ , $R_{5}$ = 60 $Ω$ and a 12V battery is connected as shown.

Calculate:
(a) the total resistance
(b) the total current flowing in the circuit. [3 MARKS]

R_{1} = 10 Ω

R_{2} = 40 Ω

R_{3} = 30 Ω

R_{4} = 20 Ω

R_{5} = 60 Ω

In the circuit diagram given below five resistances of $10 Ω, 40 Ω, 30 Ω, 20 Ω, a n d 60 Ω$
are connected in series to a 12 V battery.

Calculate :
(a) the total resistance in the circuit.
(b) the total current flowing in the circuit.

Join BYJU'S Learning Program