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ELECTRIC CIRCUITS
     
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 I1
  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, R1=3Ω and R2=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 R1
  d) the r.m.s. value of the voltage across R2
     
10.   A resistor is to be made using wire of diameter 0.2mm.
    The wire is made of nichrome of resistivity 1.5010-6m.
  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 2.4CW-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 4.0104C-1, show that the change in resistance of the resistor is unlikely to cause too many problems.
     
11.   A thermistor, Rt (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 Rt is 1.25V
    The graph shows the variation with temperature of the resistance of Rt
     
   
     
    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 = ??...
 
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