# Potential difference, Electric field, Equivalent resistance of the circuit

Please give detailed and clearly explained answers.

1. A uniform electric field E of magnitude 235 N/C is directed in the negative x direction in the Figure 1 in the attachment. The coordinate of point A are (-0.2, -0.3) m, those of point B are (0.4, 0.5) m and those of point C are (-0.2, 0.5) m.

(a) Calculate the potential difference between point A and point C.

(b) Calculate the potential difference between C and B.

(c) Calculate the potential difference between A and B.

(d) Show that the potential difference between A and B is sum of the potential difference between A and C, and the potential difference between C and B.

2. Over a certain region of space, the electric potential is given by :

V(x,y,z) = 5 z - 3 z^2 y + 2 y x^2

(a) Find the expression for the x, y and z components of the electric field over this region.

(b) What is the magnitude of the field at a point P that has coordinates (1, 0, -2)?

3. Refer to the Figure 3 in the attachment, where R1 = 4 Ohm, R2 = 24 Ohm, R3 = 6 Ohm, R4 = 8 Ohm and R5 = 24 Ohm are connected to a battery of 24 V.

(a) Find the equivalent resistance of the circuit.

(b) Find the total current.

(c) Find the current in each resistor (I1, I2, I3, I4 and I5).

(d) Find the voltage across each resistor (V1, V2, V3, V4 and V5).

(e) Find the power delivered to each resistor (P1, P2, P3, P4 and P5).

#### Solution Preview

Please refer to the attachment.

Problem 1

y

C(-0.2,0.5) B (0.4,0.5)

E = 235 N/C

x

A(-0.2,-0.3)

a) Potential difference between two points is defined as the work done in moving a unit positive charge from one point to the other without acceleration. A unit positive charge placed at A will experience a force in the direction of the electric field i.e. -x direction. As the charge is moved from point A to point C, the displacement is in +y direction i.e. the displacement is perpendicular to the direction of force; work done is zero. Hence, potential difference between points A and C is zero.

Mathematically: Work done W = E.S = ES cosθ = FS cos90O = 0

VAC = 0 ........(1)

b) Potential difference between points C and B = Work done in moving unit +ve charge from point C to point ...

#### Solution Summary

Potential differences, electric fields and equivalent resistance are examined.