Question

for resistance 10 ohm 12 12 ohm 30 ohm 40 ohm are connected in a parallel combination 220 volt find a total resistance B total current in circuit c individual current in individual resistance
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Answer 1

QUESTION

For resistance 10 ohm, 12 ohm, 30 ohm & 40 ohm are connected in a parallel combination 220 volt

• find a total resistance
• total current in circuit
• Individual current in individual resistance

ANSWER

1/Total Resistance = 1/10 + 1/12 + 1/30 + 1/40

1/Total Resistance = (12 + 10 + 40 + 30)/120

1/Total Resistance = 92/120

• Total Resistance = 120/92 Ω

V = IR

Total Current = Voltage / Resistance

Total Current = 168.67 A

• Current in 10 Ω = 220 / 10 = 22 A
• Current in 12 Ω = 220 / 12 = 18.34 A
• Current in 30 Ω = 220 / 30 = 7.34 A
• Current in 40 Ω = 220 / 40 = 5.5 A

Answer 2

• R1=10ohm
• R2=12ohm
• R3=30ohm
• R4=40ohm

$\boxed{\sf \dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\dots}$

$\\ \sf\longmapsto \dfrac{1}{R}=\dfrac{1}{10}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{40}$

$\\ \sf\longmapsto \dfrac{1}{R}=\dfrac{12+10+4+3}{120}$

$\\ \sf\longmapsto \dfrac{1}{R}=\dfrac{29}{120}$

$\\ \sf\longmapsto R=\dfrac{120}{29}$

$\\ \sf\longmapsto R=4.1\Omega$

• Voltage=V=220V
• Current=I=?

Using ohms law

$\boxed{\sf \dfrac{V}{I}=R}$

$\\ \sf\longmapsto I=\dfrac{V}{R}$

$\\ \sf\longmapsto I=\dfrac{220}{4.1}$

$\\ \sf\longmapsto I\approx=55A$