Electric circuits, Current, and resistance - Physics Department ...

Electric circuits, Current, and resistance 

(Chapter 22 and 23) 

Acknowledgements: Several Images and excerpts are taken from 

College Physics: A strategic approach, Pearson Education Inc 

Dr. Mangala Singh, 1P22/92 Brock University


Current 

If electric charge (e.g. 

electron) moves, we will say 

an electric current, I, is set 

to exist. 

I 

+ 

A 

An electric current, I, is the 

rate at which net charge (∆Q) 

flows through a surface area A 

I 

∆Q 

= ∆ t 

Current’s units = C/S and 

often written as A (Ampere) 

Electrons are actual current carriers in 

metals. They flow opposite to the direction 

of electric field or current 

Although current carriers (i.e., charges) 

could be “+” or “-”, the direction of 

current will be in the direction of a “+” 

charge flow (i.e., clockwise) 


Current and Current density 

n = number of mobile 

charges per unit volume 

q = charge on each current 

carriers 

∆x = distance they move in 

a time interval ∆t 

v d = speed (called drift 

velocity ) 

J = current density 

Drift velocity v d ? 

I 

∆ x = v ∆t 

d 

+ 

∆ Q = ( nA∆x) 

q 

= ( nAv ∆t) 

q 

I 

J 

d 

∆Q 

= = nqvd 

A 

∆t 

I 

= = nqvd 

A 

A 


Multiple choice questions 

1. The charge carriers in metals are 

A. electrons. 

B. positrons. 

C. protons. 

D. a mix of protons and electrons. 

2. A battery is connected to a resistor. Increasing the resistance of the resistor 

will 

A. increase the current in the circuit. 

B. decrease the current in the circuit. 

C. not affect the current in the circuit. 

3. A battery is connected to a resistor. As charge flows, the chemical 

energy of the battery is dissipated as 

A. current. 

B. voltage. 

C. charge. 

D. thermal energy. 


Problem: The discharge of the electric eel can transfer a charge of 2.0 mC in a 

time of 2.0 ms. What current, in A, does this correspond to? 

Solution: 

Step 1: To solve a problem, note each and every quantities mentioned in 

your problem. In this problem 

Q = 2.0 x10 -3 C 

Time = 2.0 x10 -3 s 

Current = ? 

Step 2: Identify relationship between these quantities 

Step 3: Rearrange your equation to find out the unknown quantity 

Add each and every numbers and compute. 

Warning: Calculator does what you ask for….If you insert wrong numbers or in 

a wrong manner, you will get a wrong answer!!! You must learn how to use your 

calculator properly 

I = Q/t = 2.0x10 -3 C/2.0x10 -3 s = 1A 


Batteries 

The potential difference between the 

terminals of a battery, often called 

the terminal voltage is often called 

battery’s electromotive force (emf) 

Wchem 

∆ Vbat 

= = 

q 

ξ 


Simple Circuits 

The current is determined by the 

potential difference and the resistance of 

the wire: 

I 

= 

∆ 

V wire 

R 

battery 


Ohm’s law and resistance 

A current density J & the electric field E are 

established in a conductor when a potential 

difference (V b -V a ) is maintained across the 

conductor 

J = σE ------- Ohm’s Law 

σ is called electrical conductivity of the materials 

Ohmic materials: In these materials the ratio of J 

and E is a constant “σ”. In other words, it is J 

varies linearly with E 

Value of conductivity of the materials are different for 

different materials 

V = V −V 

b 

V 

E = ⇒ V = El 

l 

V 

J = σ E = σ 

l 

l 

V = I ⇒ V = RI 

σ A 

l 

R = 

σ A 

a 

ρL 

R = 

A 


Resistance & Resistivity 

The resistance of a wire depends on its dimensions 

(length L & Cross sectional area A) and the resistivity of 

its material. 

R = 

ρL 

A 

Every material has a characteristic resistivity that only 

depends on the properties and composition of the 

material. 

Value of resistivity of the materials are different for 

different materials 

resistivity of the metal increase as temperature increase 

resistivity of semiconductors and insulators decreases 

as temperature increases 


Multiple choice 

A battery is connected to a wire, and makes a current in the wire. Which of the following changes 

would increase the current? 

(1) Increasing the length of the wire; (2) keeping the wire the same length, but making it thicker; (3) 

using a battery with a higher-rated voltage; (4) making the wire into a coil, but keeping its dimensions 

the same; (5) increasing the temperature of the wire. 

Problem 1: 

A. All of the above 

B. 1 and 5 

C. 1, 4, and 5 

D. 2 and 3 

E. None of the above 

A wire has resistance of 21 ohm. It is melted down and from the same volume of metal a new wire is 

made, that is three times longer than the original one. What is the resistance of new wire 

Problem 2: 

The filament of a 100-W bulb carries a current of 0.83 A at the normal operating voltage of 120 V. 

A. What is the resistance of the filament? 

B. If the filament is made of tungsten wire of diameter 0.035 mm, how long is the filament? 


Power in Circuits 


Energy and Power in Resistors 


Multiple choice 

A resistor is connected to a 3.0 V battery; the power dissipated in the resistor is 1.0 W. The battery is 

traded for a 6.0 V battery. The power dissipated by the resistor is now 

A. 1.0 W 

B. 2.0 W 

C. 3.0 W 

D. 4.0 W 

Problem 1: An electric blanket has a wire that runs through the interior. A current causes energy to be 

dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 

V. It dissipates a power of 82 W. What is the resistance of the wire that runs through the blanket? 


Example Problem 

An electric blanket has a wire that runs through the interior. A current causes energy to be dissipated in 

the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V. It 

dissipates a power of 82 W. What is the resistance of the wire that runs through the blanket? 

Summary 


Conservation of Current 

∑ 

I 

in 

= ∑ 

I 

out 



1. Rank the bulbs in the following circuit according to their brightness, from brightest to dimmest. 

A. A > B = C > D 

B. A = B = C = D 

C. A = D > B = C 

D. B = C > A > D 


Drawing Circuit Diagrams 


Kirchhoff’s Law 

∑ 

I 

in 

= ∑ 

I 

out 

∆ V = ∑ V = 

loop 

i 

0 


Using Kirchhoff’s Laws 



1. The diagram below shows a segment of a circuit. What is the 

current in the 200Ω resistor? 

A. 0.5 A 

B. 1.0 A 

C. 1.5 A 

D. 2.0 A 

E. There is not enough information to decide. 

2. The diagram below shows a circuit with two batteries and three resistors. What is the potential 

difference across the 200Ω resistor? 

A. 2.0 V 

B. 3.0 V 

C. 4.5 V 

D. 7.5 V 

E. There is not enough information to decide. 


Series Resistors 


Parallel Resistors 


Problems 

1. There is a current of 1.0 A in the circuit below. What is the 

resistance of the unknown circuit element? 

2. What is the current out of the battery? 


Analyzing Complex Circuits 


Problems 

1. In the circuit shown below: 

A. Rank in order, from most to least bright, the brightness of 

bulbs A–D. Explain. 

B. Describe what, if anything, happens to the brightness of bulbs 

A, B, and D if bulb C is removed from its socket. Explain. 


Problems 

In the circuit shown below: 

A. How much power is dissipated by the 12 Ω resistor? 

B. What is the value of the potential at points a, b, c, and d? 


Battery and its internal resistance (r) 

As the charges passes through 

from – to + terminal of the 

battery its potential energy 

increases 

The current in the circuit 

-Depends both external 

resistance to the battery 

-And its internal resistance 

I 

= 

ξ 

R + r 

Due to internal resistance of the 

battery, its potential decreases 

by Ir, wherein I is the current. 

Terminal voltage of the battery 

= V + 

-V - 

= ξ-Ir 

Note: Terminal voltage may exceed the emf 

by an amount Ir – when the current is 

opposite the emf as in the case of charging a 

battery with another source of emf. 

Power dissipated, P, in the load 

resistance R 

ξ 

( R + r) 

2 

P 2 

= I R = R 2 


Problems: 

1. Show that maximum power lost in the load resistor R occurs 

when R =r, i.e., when the value of load resistance matches the 

internal resistance of the battery.

Electric circuits, Current, and resistance - Physics Department ...

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