


1. 

Each of the resistors in the circuit below has a resistance R. 











What is their total resistance (in terms of R... of course!)? 



2. 
a) 
Four identical resistors are connected to
a battery of emf 12V and zero internal resistance, as shown below. 











What voltage would a voltmeter read when connected across the
following points? 


i) 
A and D 
ii) 
A and B 
iii) 
A and C 
iv) 
B and C 


b) 
A short circuit (a wire of very low resistance) is connected
across points C and D, as shown below. 











What voltage would a voltmeter now read when connected across
the same points? 


i) 
A and D 
ii) 
A and B 
iii) 
A and C 
iv) 
B and C 




3. 
a) 
Calculate the total resistance of the four resistors in the
circuit shown below. 










b) 
Calculate the total resistance of the
same four resistors when a wire of very low resistance
is connected across points X and Y. 



4. 

In the circuit below, the 24V
supply has zero internal resistance. 










a) 
Calculate the total resistance of the circuit. 

b) 
Calculate the current I 

c) 
Calculate the voltage across the points A and B. 

d) 
Calculate the current I_{1} 

e) 
How much charge will pass through the supply in 20s? 

f) 
How much energy will be converted to internal energy (thermal
energy) by the 6Ω resistor in 5 minutes? 

g) 
Calculate the power dissipated in the
8Ω
resistor. 

h) 
Calculate the total amount of energy converted to thermal energy
by all the resistors in 10 minutes. 



5. 

Calculate the maximum current which can be supplied by
each of the following batteries: 

a) 
a car battery of emf 13.2V and
internal resistance 0.15Ω 

b) 
a battery of eight cells, each of emf 1.6V
and internal resistance 0.4Ω 


NB there are various ways in which these cells could be
connected to make a battery... 



6. 

Two resistors, R_{1}=3Ω
and R_{2}=6Ω,
are connected in parallel with each other. 


They are then connected to a battery of emf 10V
and internal resistance 3Ω 


Calculate 

a) 
the current flowing through the battery 

b) 
the current flowing through the 6Ω
resistor. 



7. 

A battery of emf 6V is connected
to two 5Ω
resistors in parallel with each other. 


If the current flowing through the battery is
2A, calculate the internal
resistance of the battery. 



8. 

Three 12W
resistors are to be connected to a battery of 24V
and 2Ω. 


Draw circuit diagrams showing how the resistors should be
connected in order that the current flowing through the battery is 

a) 
4A 

b) 
1.2A 

c) 
0.63A 

d) 
2.4A 



9. 

This question is about r.m.s. currents and voltages. 











For the circuit shown above calculate 

a) 
the r.m.s. value of the current, I 

b) 
the maximum value of the current 

c) 
the mean power dissipated in R_{1} 

d) 
the r.m.s. value of the voltage across R_{2} 



10. 

A resistor is to be made using wire of diameter 0.2mm. 


The wire is made of nichrome of resistivity 1.50×10^{6}m. 

a) 
Calculate the length of wire needed to make a resistor of
resistance 15.0Ω 

b) 
The diameter of the wire was measured using a Vernier caliper
having a precision of ±0.02mm. 


what is the uncertainty in the value of the resistance made
using the wire (state your answer in the usual way, that is, in the
form, resistance = R ±δR). 


Ignore any other sources of uncertainty in this calculation. 

c) 
Calculate the power dissipated in the resistor when a current of
1.5A flows through it. 

d) 
The resistor is found to change temperature by 2.4°CW^{1}
of power dissipated. 


After the current (1.5A) has
been flowing for a few minutes, the temperature of the resistor will
have increased. 


Given that the temperature coefficient of resistance of nichrome
is 4.0×10^{−4}°C^{1},
show that the change in resistance of the resistor is unlikely to
cause too many problems. 



11. 

A thermistor, R_{t} (temperature dependent resistor) is
to be used in a potential divider circuit as part of a thermostat. 


The heater is switched on (by circuits not shown) when the
voltage across R_{t} is 1.25V 


The graph shows the variation with temperature of the resistance
of R_{t} 











Find the approximate temperature at which the heater will switch
on 

a) 
with R=9kΩ 

b) 
with R=18kΩ 



12. 

A battery has an emf, E
, and internal resistance, r. 


The battery is
connected to a variable resistor, R, as shown below. 










a) 
As the variable resistor is varied, the power dissipated in it
will also vary. 


Show that the power, P, dissipated in the variable resistor is
given by 







b) 
If E=9V and
r=3Ω,
what is the maximum value of the power dissipated in the variable
resistor, R? 


NB 


If you know a mathematical method for finding the maximum value
of a function, ok, use that. 


If not, how about making a guess as to what value of R
will result in the maximum power being supplied to it. 


If R >> r then the power dissipated in the variable resistor is
very low (try, say, R = 300Ω). 


Similarly, if R << r, P is very low (try, for example, R = 0.03Ω). 


So, how about R = ??... 