The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Each of the rectangular pieces is made from a material whose resistivity is p = 1.50 x 102 Q2*m, and the unit of length in the drawing is Lo = 3 cm. Each piece of material is connected to a 3.00-V battery. Find (a) the resistance and (b) the current in each case. 2LO (a) م41 ALO 2LO ALO 2LO Lo (c) (b)

Wires A and B, having equal lengths of 40.0 m and equal diameters of 2.94 mm, are connected in series. A potential difference of 62.9 V is applied between the ends of the composite wire. The resistances are RA = 0.0996 Q and RB = 0.570 2. For wire A, what are (a) magnitude J of the current density and (b) potential difference V? (c) Of what type material is wire A made (see the table below)? For wire B, what are (d) J and (e) V? (f) Of what type material is B made? Resistivities of Some Materials at Room Temperature (20°C) Resistivity, p (N m) Temperature Coefficient of Resistivity, a (K¯') Material Typical Metals 4.1 x 10-3 4.3 x 10-3 Silver 1.62 x 10-8 Copper 1.69 × 10-8 4.0 x 10-3 4.4 x 10-3 Gold 2.35 x 10-8 Aluminum 2.75 x 10-8 Manganin" Tungsten Iron 4.82 x 10-8 0.002 x 10-3 5.25 x 10-8 4.5 x 10-3 6.5 x 10-3 3.9 × 10-3 9.68 x 10-8 Platinum 10.6 x 10-8 Typical Semiconductors 2.5 x 103 Silicon, pure Silicon, n-type Silicon, p-type -70 x 10-3 8.7 x 10-4 2.8 x 10-3 Typical Insulators…

There is a potential difference of 0.90 V between the ends of a 20 cm long graphite rod that has a cross-sectional area of 1.8 mm2. The resistivity of graphite is 7.5 x 10-6 2-m. (a) Find the resistance of the rod. (b) Find the current. (c) Find the electric field inside the rod.

A gold wire has a length of 23.0 m and a resistance of 4.70 Ω at 20.0°C. Assuming a circular cross-section, what is the wire's diameter (in mm)? The resistivity of gold at 20.0°C is 2.44 ✕ 10−8 Ω · m