Concept #1: Resistors and Ohm's Law

Practice: A resistor has a current through it of 5 A. If the EMF across the resistor is 10 V, what is the resistance of this resistor?

Example #1: Current Through Unknown Resistor

Practice: Two resistors are made of the same material, one twice as long as the other. If the current through the shorter resistor is 5 A, what is the current through the longer resistor if they both have the same potential difference?

If a cylindrical metal wire is stretched to 4 times of its original length, what is the resulting resistance R, compared with the original resistance R0?
A) R = 16R0
B) R = R0/16
C) R = R0/4
D) R = 4R0

You are given a copper bar of dimensions 3 cm x 5 cm x 8 cm and asked to attach leads to it in order to make a resistor. If you want to achieve the SMALLEST possible resistance, you should attach the leads to the opposite faces that measure
(a) 3 cm x 8 cm.
(b) 5 cm x 8 cm.
(c) 3 cm x 5 cm.
(d) Any pair of faces produces the same resistance.

Two pieces of metal are shaped into resistors and are connected end-to-end. The first resistor, R1, has twice the length of the second resistor, R 2, but an equal diameter. If the resistors are made of the same material, and are connected to a voltage source, what is the ratio of the voltage across each resistor, V1 / V2 ?

The headlight of a car has a resistance R = 3.4Ω. The headlight consists of a tungsten wire (resistivity p = 5.6 x 10-8 Ω • m) of length 12.4 cm. What is the cross-sectional area of the wire?

The current in a resistor decreases by 2.27 A when the voltage applied across the resistor decreases from 12.3 V to 4.26 V. Find the resistance of the resistor.
1. 0.892638
2. 4.37778
3. 7.76768
4. 3.54185
5. 2.65823
6. 4.25074
7. 4.50218
8. 3.12424
9. 3.48214
10. 5.13265

What is the resistance of a Nichrome wire at 0.0°C if its resistance is 100.00 Ω at 45°C? The temperature coefficient for nichrome is 4.00x10-4 (°C)-1A. 100.5 ΩB. 100.0 ΩC. 98.23 ΩD. 96.46 ΩE. 94.23 Ω.

A long, uniform conducting wire with resistance R is connected to the terminals of a battery with emf V, dissipating a power P. If the cross-sectional area of the wire is halved, what is the new total power dissipated?A. 2PB. ¼ PC. 4PD. ½ PE. P

Consider two conductors 1 and 2 made of the same ohmic material (ρ 1 = ρ2). Denote the length of the conductor by ℓ and the radius by r. The same voltage V is applied across the ends of both conductors. If r2 = 2 r1 , and ℓ2 = 2 ℓ1 , find the ratio I 2 / I1 of the currents.
1. I2 / I1 = 8
2. I2 / I1 = 1/2
3. I2 / I1 = 1
4. I2 / I1 = 1/4
5. I2 / I1 = 1/8
6. I2 / I1 = 2
7. I2 / I1 = 4

The length of a certain wire is doubled and at the same time its radius is increased by a factor of 4. What is the change in the resistance of this wire?A) It is reduced by a factor of 8.B) It increases by a factor of 4.C) It increases by a factor of 8.D) It is reduced by a factor of 4.

The resistivity of a 1.0 m long wire is 1.72 x 10 -8 Ωm and its cross-sectional area is 2.0 x 10-6 m2. If the wire carries a current of 0.2 A, what is the voltage across the wire?