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Current Electricity Circuits

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Current Electricity Circuits - Lesson Summary



An electric circuit is a closed path for flow of electricity through which electricity can be converted into different forms of energy. An electric circuit basically contains a source of electricity, a load resistance, a switch or a key for making the circuit on or off at ones convenience (which makes or breaks the circuit correspondingly).

The diagrammatic representation of an electric circuit is called the circuit diagram. Each electric component in a circuit has a unique symbol through which it is represented in a circuit diagram. If a circuit is switched off, it is called an open circuit and if the circuit is switched on it is called a closed circuit.

The reciprocal of the net resistance of a number of resistors connected in parallel is the sum of the reciprocals of the individual resistances.

The resistivity of an alloy is generally higher than that of its constituent metals. Alloys do not oxidise (burn) readily at high temperatures. For this reason, they are commonly used in electrical heating devices, like electric iron, toasters etc. Tungsten is used almost exclusively for filaments of electric bulbs, whereas copper and aluminium are generally used for electrical transmission lines.
 
In various electrical gadgets, we often use resistors in various combinations. There are two methods of joining the resistors together.
 
Series Combination of Resistors
If a number of resistors are joined end to end in an electric circuit, the resistors are said to be connected in series.
 
In a series combination of resistors the current is the same in every part of the circuit or the same current flows through each resistor, i.e., there is only one path for the flow of current. 
 
Let us consider a circuit in which three resistors R 1, R 2 and R 3 are connected in series with a battery of potential difference V. The potential difference V is equal to the sum of potential differences V 1, V 2, and V 3. That is the total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors. That is,
V = V 1 + V 2 + V 3 ------------ (i)
 
Let I be the current through the circuit. The current through each resistor is also I. It is possible to replace the three resistors joined in series by an equivalent single resistor of resistance R s, such that the potential difference V across it, and the current I through the circuit remains the same.

Applying the Ohm’s law to the entire circuit,
V = I R s. ------------------- (ii)

On applying Ohm’s law to the three resistors separately,
V 1 = I R 1;    V 2 = I R 2;   and V 3 = I R 3.  ------------------- (iii)
From the eaquations (i),(ii) and (iii)
I R s = I R 1 + I R 2 + I R 3 implies that
R s = R 1 +R 2 + R 3.

When several resistors are joined in series, the resultant resistance of the combination Rs equals the sum of their individual resistances, R 1, R 2, R 3.

Note: Rs is greater than any individual resistance.
 
Parallel Combination of resistors
In a parallel circuit each resistor is placed in its own separate branch.  A parallel circuit provides multiple paths for the current to flow.
 
Consider the arrangement of three resistors joined in parallel with a  battery.  It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.
I = I 1 + I 2 + I 3 --------------- (i)
 
The potential difference across each resistor is the same and is equal to the voltage of the battery.
 
Let R p be the equivalent resistance of the parallel combination of resistors. By applying Ohm’s law to the parallel combination of resistors,
I =  V R p     --------------- (ii)

On applying Ohm’s law to each resistor,
I 1 =   V R 1   ; I 2 =    V R 2     ; and I 3 =   V R 3   --------------- (iii)

From the equations (i), (ii) and (iii)

   V R p     =   V R 1   +   V R 2 +    V R 3   

or    1 R p   =    1 R 1   +   1 R 2 +   1 R 3   .
 
The reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.

Note:  The effective resistance in a parallel circuit is always less than the lowest resistance in the circuit.
 
In a series circuit the current is constant throughout the electric circuit. Thus it is obviously impracticable to connect an electric bulb and an electric heater in series, because they need currents of widely different values to operate properly. Another major disadvantage of a series circuit is that when one component fails the circuit is broken and none of the components works. For example, the electrician has to spend lot of time in trouble-locating and replacing the ‘dead’ bulb in a series of decorative bulbs– each has to be tested to find which has fused or gone.

On the other hand, a parallel circuit divides the current through the electrical gadgets. The total resistance in a parallel circuit is decreased. This is helpful particularly when each gadget has different resistance and requires different current to operate properly.                               Ohmic Conductors                           Non-Ohmic Conductors 1. Conductors that obey Ohm’s Law are called Ohmic conductors.

2. In Ohmic conductors, current is proportional to voltage.

3. Magnitude of current remains unchanged when current or voltage is reversed in Ohmic conductors.

4. In Ohmic conductors, temperature affects current and resistance. 1. Conductors which do not obey Ohm’s Law are called Non-Ohmic conductors.

2. In Non-Ohmic conductors, current is not proportional to voltage.

3. Magnitude of current changes when current or voltage is reversed in Non-Ohmic conductors.

4. In Non-Ohmic conductors, different factors affect current and resistance.

Laws of Electric Resistance
1. The resistance (R) of a conductor of a given material is directly
Proportional to its length (l)
Rα l ----------------- (i)

2. The resistance (R) of a conductor of a given material is inversely
Proportional to its area of cross section (A)
Rα  1 A     ----------------- (ii)

From the equations (i) and (ii)
R =   ρl A    , where ρ is called the resistivity of the material of unit length and unit cross-sectional area.

It is measured in ohm-meter. It is independent of the length or cross-sectional area of the conductor.

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