Resistors in Series and Parallel
Introduction
In a circuit, there is normally there is more than one resistor and these resistors are combined in different ways. These combinations can be seen as a series connection or parallel connection and/or a combination of the two. Series combination of more than one resistor is the one in which the current flowing through both the resistors is the same and voltage across the individual resistor may be different. Suppose two resistors R1 and R2 are connected in series then their equivalent resistance is given by Req = R1 + R2. The current in both the resistor will be I = V/Req; where V is the supply voltage and the potential drop across the resistors will be I*R1 and I*R2. The value of Req in the case of a series connection is higher than the highest individual resistor.
When the two resistors are connected in parallel, then-current through both the resistors may not be the same but potential drop across both the resistors is the same. The equivalent resistance of two resistors R1 and R2 in parallel combination is given by (1/Req) = (1/R1) + (1/R2). Current in the circuit will be I = V/Req; current through R1 will be (V*R2)/Req and that through R2 will be (V*R1)/Req; here V is the supply voltage. The value of Req in the case of a series connection is lower than the lowest individual resistor.
A simple experiment to explore the parallel and series connection of resistors is described below.
Design of Experiment
Two unknown resistors, a DC source, an ammeter, voltmeter wires, and a switch is all that are required. First, a series connection of the two resistors will be made and the ammeter and the switch will also be connected in series. The switch will be put on and the current will be recorded. Using a voltmeter, potential drop across either of the resistors and the DC supply will also be measured. These values will help in calculating R1, R2, and Req.
In another setting, the same resistors will be connected in parallel, the circuit current, and the potential drop across both the resistors will be measured. BY changing the position of the ammeter current through the individual resistors will also be measured.
Data and Results
A virtual experiment was done to measure the current through and the potential drop across unknown resistors and their series and parallel combinations. The data is presented below in table 1.
Table 1: Data and results of the series and parallel combinations of two unknown resistors.
Discussion & Conclusion
Based in the findings of the experiment the resistance of the resistor and the bulb is the same and its value is 10Ω. A Series combination of resistors produces a bigger resistor. In this case, a resistor and a bulb of 10Ω each when combined in series have produced an equivalent resistance of 20Ω, which is in line with the hypothesis. On the other hand, the parallel combination of a resistor and a bulb of 10Ω each has produced an equivalent resistance of 5Ω; thus leading to a drop in resistance.
Both the circuits do not have identical currents. The circuit has two resistors in series has a current of 0.45A flowing through it and the current in the individual resistors is also 0.45A only. In the circuit having a parallel connection, the circuit current is 1.8A while the current flowing through either resistors is 0.9A.
The Effect of Number of Turns of a Solenoid on the Magnetic Field
Introduction
When a current carrying wire forms a loop, it is called a solenoid. It is a very good device to produce uniform magnetic field in a cylindrical region. Magnetic field inside a solenoid is given by B = Ωni; where m is the permeability constant, n is number of turns of the solenoid and I is the current through the solenoid. From this expression it is obvious that magnetic field due to a solenoid is directly proportional to the number of turns it has. A simple experiment can be designed to investigate the effect of number of turns on the magnetic field due to a solenoid and also effect of distance on the magnetic field due to a solenoid. Such an experiment is described below.
Design of Experiment
Three solenoids with 1, 2 and 3 turns, a DC supply of known voltage, a magnetic field meter and a compass is all that is required to carry out this experiment. The circuit will be completed by connecting the DC supply to the wires of the solenoid and the magnetic field will be measured at certain location near the solenoid on its axis. Direction of the magnetic field will also be recorded. The value and direction of the magnetic field will be measured again by reversing the direction of current. These experiments will be repeated with the solenoids of 2 turns and 3 turns. Same measurements will be made again by moving the magnetic field meter away along the axis of the solenoid and these values will be recorded.
Data and Results
A virtual experiment was carried out to investigate effect of number of turns of a solenoid on the magnetic field due to it. The measurements were made at two locations along the axis of the solenoid to investigate effect of distance on the magnetic field. Effect of the direction of current on the direction of magnetic field was also investigated by changing the direction of current. The experimental data is presented below in table 1.
Table 1: Magnetic field due to a solenoid.
The graph between magnetic field and number of turns of a solenoid at two locations is presented below in figure 1.
Discussion & Conclusion
From the experimental data (table 1 and 2) and also from the figure 1 it can be clearly seen that magnetic field due to a solenoid is directly proportional to the number of turns of the solenoid. This is consistent with the theoretical relationship B = Ωni; where m is the permeability constant, n is number of turns of the solenoid and I is the current through the solenoid.
Magnetic filed due to a solenoid drops as one moves away from a solenoid. This is a typical character of different fields. Generally strength of a field is more near the source and the sink and drops as one moves away.
Direction of magnetic field is related to the direction of current in a solenoid. To find the direction of magnetic field one should try to fold the four fingers of his/her right hand in the direction of the current, then the stretched thumb gives the direction of the magnetic field.
Electromagnetic Induction
Introduction
When a bar magnet or a current carrying loop (electromagnet) is brought near a conducting loop a current is induced in the conducting loop. This phenomenon is referred as electromagnetic induction. The magnitude of the induced emf in the conducting loop is equal to the rate of change of magnetic flux through it and direction of the induced current is such that it opposes the change of magnetic flux through it (Lenz law).
An experiment can be set up to investigate electromagnetic induction in a conduction loop.
Design of Experiment
A conducting loop, a voltmeter, a bar magnet and a current carrying loop is all that is required for this experiment. The voltmeter will be attached to the conducting loop. Now the bar magnet will be brought near the loop along its axis keeping its north pole towards the loop. The readings of the voltmeter will be recorded. The experiment will be repeated by changing the speed of the approach of the magnet. Now the direction of the magnet will also be changed and the experiment will be repeated. The readings of the voltmenter will be recorded each time. These experiments will then be repeated with the current carrying coil (electromagnet). In this case the direction of current will be changed and also the velocity of approach of the electromagnet towards the conducting loop will also be varied.
Data and Results
The electromagnetic induction experiments were carried out in a virtual setting using a bar magnet and an electromagnet. Effect of the speed of approach and direction of the magnetic field was investigated. The observation of induction by a bar magnet is presented below in table 1.
Table 1: Experimental observation of electromagnetic induction by a bar magnet.
The observation of induction by an electromagnet (current carrying coil) is presented below in table 2.
Discussion & Conclusion
From the observations it was found that speed of motion has direct bearing on the magnitude of the induced emf. It did not make any difference whether the magnet was moved or the coil was moved all that mattered was the relative velocity. Changing the direction of the bar magnet has opposing effect on the sign of the induced emf. The voltage meter readings revealed that there was indeed electromagnetic induction by the bar magnet on the conduction loop and magnitude of this induction was directly related to the relative speed of the two. There was no induction in static condition. Therefore, to achieve electromagnetic induction there should be relative velocity between a magnet and a conducting loop.
Direction of the induced emf was such that it opposed the change in the magnetic field flux through the conducting coil. The magnitude of the induced current was directly related to the relative speed between the conducting loop and the magnet.
Photoelectric Effect
Introduction
When photon is made to shine a metallic surface electrons are emitted. This phenomenon is termed as photoelectric (photon + electron) effect. This phenomenon was first discovered by Hertz and was explained by none other than Albert Einstein by using dual (wave and particle) nature of light and by hypothyzing a particle character for light (photon) through his Noble winning work.
In metallic materials there is a cloud of conduction electrons which are loosely bonded to the lattice with very small binding energies of the order of a few electron volts and when a photon with energy higher than the binding energy of the electron strike the metallic surface it breaks the electron free from the surface with the excess energy manifesting as kinetic energy of the librating electron. Thus there is a minimum frequency requirement of the light to be capable of effecting photoelectric effect. The frequency should be such that energy of the incident photon is more than the binding energy of the electron. The energy balance can be written as Ephoton (hf) = BE + KEmax. A simple experiment can be designed to investigate the photoelectric effect. The experiment is briefly described below.
Design of Experiment
Cathode tube with sodium target, a variable DC source, an ammeter, and light source with filters for different frequencies is all that is required. A circuit will be constructed by connecting the cathode tube, DC source and the ammeter in series. Now the cathode will be shined with light of chosen frequency. The current will be seen in the ammeter. Now reverse voltage or stopping voltage will be applied to just stop the current. This stopping voltage will be recorded corresponding to a particular wavelength. This stopping voltage corresponds to the KEmax at that frequency of light for sodium. The experiment will be repeated with lights of different frequencies. This experiment will be repeated with cathode tubes having other elements like Ca, Zn, Cu etc as target.
Data and Results
A virtual experiment was carried out to investigate photoelectric effect in sodium, calcium, zinc, copper and platinum. The experimental data and calculations pertaining to photoelectric effect in sodium are presented in table 1 below.
Table 1: Data and calculated values for photoelectric effect in sodium
The plot between maximum kinetic energy and frequency of the light is presented below in figure 1.
The threshold frequency of light to cause photoelectric effect in different elements like sodium, calcium, copper, zinc and platinum is presented in table 2 below:
Table 2: Threshold frequency for causing photoelectric effect in different elements.
Discussion & Conclusion
From the graph in figure 1 it can be estimated that threshold frequency of light to cause photoelectric effect in sodium is 5.69825E+14 Hz. This corresponds to the binding energy or work function of 3.8×10-19 J for electrons in sodium. Using data in table 2, the work function of sodium is 3.7×10-19 J. The accepted value for work function of sodium is 3.65×10-19 J. The error calculation is presented below:
Work function estimation from the graph 1:
Standard error = 0.15×10-19 J Absolute error = 0.041
Work function estimation from the table 2:
Standard error = 0.05×10-19 J Absolute error = 0.014
Stopping potential and the wavelength: Smaller the wavelength, greater the energy of the incident photon and therefore, greater is the maximum kinetic energy of the photoelectrons and greater will be the stopping potential. The reverse is also true. Thus wavelength of the incident photon has an opposing relationship with the stopping potential.