Question

Two wires A and B are of equal length and have equal resistance. If the resistivity of A is more than that of B which wire is thicker and why? For the electric circuit given below calculate: (i) Current in each resistor, (i) Total current drawn from the battery, and (iii) Equivalent resistance of the Circuit
Circuit: see attachment( voltage 6V)​

Answer 1

Answer:

1) Wire B is more thicker than A because resistance is inversely proportional to thickness. B has less resistance than A, so it must be thicker than A.

2)(i) Let the resistors be R1(20Ω), R2(10Ω) and R3(5Ω)

Current through R1= 6/20= 0.3A

Current through R2= 6/10= 0.6A

Current through R3= 6/5= 1.2A

(iii) As, R1, R2 and R3 are connected in parallel,

1/Rp=1/R1+1/R2+1/R3

=>1/Rp=1/20+1/10+1/5

=>1/Rp=1+2+4/20

=>1/Rp=7/20

=>Rp=2.86(approx)

(ii) Total current= 6/2.86= 2.1(approx)

Answer 2

Wire A is thicker than wire B.

(i) Current in resistors 30Ω, 10Ω, and 5Ω are 0.2A, 0.6A, and 1.2A.

(ii) The total current draw from the battery is 2A

(iii) The equivalent resistance of the circuit is 3Ω.

• The resistance R of a wire with length l, area of cross-section A and resistivity of the material of the wire ρ is given by the formula:

        R = ρl/A

• Since given that $l_A = l_B$ and $R_A=R_B$,

      ⇒ R and l are constants for this situation,

     ⇒ A ∝ ρ

• Since $\rho_A>\rho_B$

       ∴ $A_A > A_B$

• Hence, wire A is thicker than wire B.

(i) The current in each resistor using Ohm's law is as follows:

In 30Ω resistor, I₃₀ = 6 / 30 = 0.2 A

In 10Ω resistor, I₁₀ = 6 / 10 = 0.6 A

In 5Ω resistor, I₅ = 6 / 5 = 1.2A

(ii) The total current in the circuit = I₃₀ + I₁₀ + I₅

= 0.2 + 0.6 + 1.2

= 2A

(iii) All the three resistors in the circuit are arranged in parallel,

⇒ 1/R = 1/30 + 1/10 + 1/5

or 1/R = 1 + 3 + 6 / 30

= 1 / 3

⇒ R = 3Ω