Question

Three resistors of 10, 20 and 30 ohms are connected in parallel to a 9v battery. Calculate: [3] (a) value of current through each resistor (b) total current in the circuit (c) total effective resistance of the circuit

Answer 1

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Answer 2

Answer:

a) current through each resistor

I1 = 0.9 A , I2= 0.45A , I3 = 0.3A

b) Total current in the circuit is ,

Thus, total current flowing through the circuit is  1.65 A

c) Effective resistance

Thus, the effective resistance of the circuit is 5.45Ω

Explanation:

a) current through each resistor

For parallel combination of resistor , potential difference across each resistor is same current through 10 Ω resistor is,

V = IR

V= 9v

R = 10 Ω

Thus , I1= 9/10 = 0.9 A

Current through 20 Ω resistor ,

I2 = 9/20 = 0.45A

Current through 30Ω resistor ,

I3 = = 9/30 = 0.3 A

I1 = 0.9 A , I2= 0.45A , I3 = 0.3A

b) Total current in the circuit is ,

I  = I1 + I2+ I3

   =0.9+0.45+0.3

    = 1.65 A

Thus, total current flowing through the circuit is  1.65 A

c) Effective resistance

Thus,

$\frac{1}{Rp} = \frac{1}{10} +\frac{1}{20} +\frac{1}{30}$

$\frac{1}{Rp} = \frac{11}{60}$

Thus,

Rp = 5.45Ω

Thus, the effective resistance of the circuit is 5.45Ω