Using thick connecting wires which are very good conductors, a nichrome wire (\'

Question

Using thick connecting wires which are very good conductors, a nichrome wire ('wire 1") of length L1 and cross-sectional area Ai is connected in series with a battery and an ammeter (this is circuit 1). The reading on the ammeter is I1. Now the nichrome wire is removed, and replaced with a different wire ("wire 2") which is 2.5 times as long and has one fith the cross sectional area of the original wire (this is circuit 2). In the following questions, a subscript "1" refers to circuit 1, and a subscript "2" refers to circuit 2. It will be helpful to write out your solutions to the following questions algebraically before doing numerical calculations. (Hint: think about what is the same in these two Circu circuits.) 2-4 arta of cross sre+.onA. area of Cross echonA What is the value of the ratio I2/1? L. .. : ,a.sp L 5 o currentsin the botm eir What is the value of the ratio (R2/R1)? R2/R1 = L What is the value of the ratio of the electric fields inside the wires in the steady state? L. Additional Materials Show My Work (Optional) 2 d2 2.5 dy

Explanation / Answer

Resistance of wire,

R = rho L / A

and I = V / R = V A / rho L

I2 / I1 = (V A2 rho L1) / (V A1 rho L2)

= (A2/A1)(L1/L2)

= (1/5)(1/2.5)

= 0.08 ....Ans

R2 / R1 = (rho L2 A1 / rho L1 A2)

= (L2 / L1)(A1/A2)

= 2.5 x 5

= 12.5 ....Ans

E = V / L

E2 / E1 = (L1 / L2) = 1/2.5

= 0.4 ....Ans

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