Determine The Magnitude Of The Current In The (A) 8.0- And (B) 2.0-? Resistors In The Drawing.

Example 12.8 - Chapter 12 Class 10 - Electricity (Term 2)

Last updated at Aug. 6, 2019 by Teachoo

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 havebeen connected to a battery of 12 V. Calculate

(a) the current through each resistor,

(b) the total current in the circuit, and

(c) the total circuit resistance.

Transcript

Example 12.8 In the circuit diagram given in Fig. 12.10, suppose the resistors R1, R2 and R3 have the values 5 Ω, 10 Ω, 30 Ω, respectively, which have been connected to a battery of 12 V. Calculate (a) the current through each resistor, (b) the total current in the circuit, and (c) the total circuit resistance. Given, R1 = 5 Ω R2 = 10 Ω R3 = 30 Ω Potential difference = V = 12 V We know that, in a parallel connection The potential difference across each resistor is same. The current across each resistor is different By ohm's law, V = I R 𝑉/𝑅 = I I = 𝑉/𝑅 Finding current through each resistor R1 = 5 Ω I1 = 𝑉/𝑅_1 = 12/5 = 2.4 A R2 = 10 Ω I2 = 𝑉/𝑅_2 = 12/10 = 1.2 A R3 = 30 Ω I3 = 𝑉/𝑅_3 = 12/30 = 0.4 A (b) Total current in the circuit In parallel connection, Total current through the circuit = Sum of current through each resistor = I1 + I2 + I3 = 2.4 + 1.2 + 0.4 = 4A (c) Total circuit resistance In parallel connection, Total resistance is given by 1/𝑅 = 1/𝑅_1 + 1/𝑅_2 + 1/𝑅_3 1/𝑅 = 1/5 + 1/10 + 1/30 1/𝑅 = (6 + 3 + 1)/30 1/𝑅 = 10/30 R = 30/10 R = 3 Ω Thus, Current through each resistor I1 = 2.4 A I2 = 1.2 A I3 = 0.4 A (b) Total current is 4 A (c) Total Resistance = 3 Ω