In the circuit diagram given in fig. 12.10, suppose the resistors $R_{1}$ , $R_{2}$ and $R_{3}$ have the values $5 Ω, 10 Ω, 30 Ω$ respectively, which have been connected to a battery of 12V. calculate (a) the current through each resistor, (b) the total current in the circuit, and (c) the total circuit resistance.

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Solution

(a)As all the resistances are in parallel the voltage across each of them will be same =12V
$I_{1} = \frac{V}{R_{1}} = \frac{12}{5} = 2.4 A$

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

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

(b) Total current= $I_{1} + I_{2} + I_{3} = 2.4 + 1.2 + 0.4 = 4 A$

(c) Total circuit resistance = $\frac{V}{Total current} = \frac{12}{4} = 3 Ω$

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In the circuit diagram given in fig. 12.10, suppose the resistors R1 , R2 and R3 have the values 5Ω,10Ω,30Ω respectively, which have been connected to a battery of 12V. calculate (a) the current through each resistor, (b) the total current in the circuit, and (c) the total circuit resistance.

(a)As all the resistances are in parallel the voltage across each of them will be same =12VI1=VR1=125=2.4AI2=VR2=1210=1.2AI3=VR3=1230=0.4A(b) Total current= I1+I2+I3=2.4+1.2+0.4=4A(c) Total circuit resistance =VTotal current=124=3Ω