Patterns of problems

## Electricity

- Let's decode the pattern of questions
1
Pattern: Analysis of Ohm's Law
Description: Ohm's Law is primary to all the recurring concepts in electricity. The electrical nature of a circuit element can be determined by its V-I graph. Basic problems related to voltage and current dependence of a wire are common in short answer questions. Comparison of resistances by comparing their V-I characteristics also forms an interesting pattern of questions that you should look out for in the exam.
How to approach:
According to Ohm's Law, voltage is directly proportional to the current flowing through a circuit, provided temperature remains the same. So the V-I characteristics of resistance should be a straight line and not otherwise.
The slope of the V-I graph gives the resistance of a circuit. Higher the slope, the higher is the resistance.
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2
Pattern: Series and parallel combination of Resistors
Description: In a series circuit, all components are connected end-to-end, forming a single path for current flow. In a parallel circuit, all components are connected across each other, forming exactly two sets of electrically common points, both have their pros and cons and are used accordingly. Problems based on the equivalent resistance of a network of circuits, current and voltage division in each branch of a network are frequently observed in question banks.
How to approach:
Keep in mind, in the series network, the individual resistances are added up and in the parallel network, the reciprocal of equivalent resistance is the sum of the reciprocals of individual resistances. In the case of combined networks, look for endpoints to segregate between series and parallel networks.
In series networks, the current through each resistor is the same, only voltage across each resistor can vary. The voltage appearing on each resistor depends on its resistance.
However, in parallel networks, the voltage across each resistor remains the same. The current through each branch varies according to the resistance.
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3
Pattern: Potential Difference: Definition, units & Problems
Description: Electric Potential difference is the driver of electric current in any closed circuit. Questions can be asked from the definition of electric potential, its S.I. unit, and basic numerical problems.
How to approach: Always remember, whenever a charge is moved in a region with a potential difference, work is done by the charge. When electrons move inside a wire, connected to a cell, the potential difference of the cell drives the electron to move towards the positive terminal of the cell. The work done by a charge , in moving across a region of a potential difference , is:
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4
Pattern: Variation of Resistance with the change in dimensions of the resistor.
Description: Resistance of an element is dependent on the dimensions of the element. The resistance of a wire is directly proportional to the length of the wire and inversely proportional to the area of cross-section. A very common pattern of problems is deducing the resistance of an element after its dimensions have been altered.
How to approach:
Always remember, when a wire is remolded/stretched the volume of the wire is constant. Now find the new dimensions of the wire, both length and radius before deducing the new resistance.
Incorporate the change in dimension in both length and radius of wire in the expression for the resistance of the wire:
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5
Pattern: Heat generated in Electric Appliances
Description: Whenever an electric current flows through a resistor, energy is dissipated in the form of light and heat. There are myriads of application of the heating effect of current in daily life. Some commonly asked questions from this concept include listing applications of heating effect of current ( iron, incandescent bulbs, etc.) and quantifying the heat generated by appliances.
How to approach:
The heat dissipated in a resistive circuit of resistance R is with a current for time is given by,
The above expression can be rewritten in different forms,
Such expressions can be handy for several kinds of numerical problems.
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6
Pattern: Energy Consumption of Appliances in kWh
Description: You must have heard about your parents talking about the household power consumption in units. Now you know what units are. It is the commercial unit of energy, more specifically, kilowatt-hour(kWh). Problems related to daily/monthly/yearly energy consumption of appliances in terms of kWh have been routinely asked in exams, so you better not miss this concept.
How to approach:
1 kWh means the power consumed by an appliance of power rating 1kW in 1 hour. Hence while calculating energy in hours make sure the units of power are in kW and time in hours.
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