## Current Electricity

## Electric Current and Ohm’s Law Electric Current

Electric current can be compared with the flow of water or the flow of heat. If there is a difference in the level of water in two vessels connected by a pipe, water moves from the higher level to the lower one. Similarly, if there is a difference in temperature between two bodies connected by a thermal conductor, heat flows from the body having a higher temperature to the body with having a lower temperature. Similarly, if there is a potential difference between two charged bodies and if they are connected by an electrical conductor, positive charge moves from the body at higher potential to the body at lower potential until equilibrium is reached

The two vessels A and B are connected by pipe C. If there is a difference in water levels in the two vessels, water flows through the pipe C. The two bodies A and B are connected by tire rod C. If there is any difference in temperature between the two bodies, heat flows through rod C, until the temperature difference is reduced to zero.

Similarly, two charged bodies A and B are connected by a conducting wire C. If there is a difference of potential between the two bodies, electric charge flows through the connecting wire C, until a common potential is attained.

**Read and Learn More Class 12 Physics Notes**

**Definition:** The flow of electric charge through a conductor is called electric current. Current strength or simply current in a conductor is defined as the net flow of charge in unit time through any cross-section of the conductor

Therefore, current (I) = \(\frac{{charge}(Q)}{\text { time }(t)}\)

∴ I = \(frac{Q}{t}\)

or, Q = It

When the rate of flow of charges through any cross-section of a conductor is not uniform then the current varies with time. In this case, current will be a function of time, i.e., I The instantaneous current (i) is defined as,

i = \(\frac{dQ}{dt}\)

We can find the net charge that passes through a cross-section in a time interval extending from 0 to t, by integration. Thus,

⇒ \(Q=\int d Q=\int_0^t i d t\)

Unit of electric current: According to the above definition of current,

unit of current = \(\frac{unit of charge}{unit of time}\)

i.e., \(1 \text { ampere }=\frac{1 \text { coulomb }}{1 \text { second }}\)

or, coulomb = ampere x second

So, the current flowing through a conductor is said to be 1 ampere (A) if 1 coulomb (C) of charge flows through its cross section 1 second (s).

## Current Electricity

## Electric Current and Ohm’s Law Electric Current Numerical Examples

**Example 1. Current flows through a wire depend on time as follows: I = 3t²+ 2t+5. How much charge flows through the cross-section of the wire from t = 0 to t = 2 s?**

**Solution:**

The charge flowing through the cross-section of the wire is

⇒ \(Q=\int_0^2 I d t=3 \int_0^2 t^2 d t+2 \int_0^2 t d t+5 \int_0^2 d t\)

⇒ \(3\left[\frac{t^3}{3}\right]_0^2+2\left[\frac{t^2}{2}\right]_0^2+5[t]_0^2\)

= 22C

**Example 2. If a current I = 4πsinπt ampere flows through a wire, then find the amount of charge that flows through the wire in**

**t = 0 to t = Is****t = 1s to t = 2s.**

**Solution:**

⇒ \(Q=\int_{t_1}^{t_2} I d t=4 \pi \int_{t_1}^{t_2} \sin \pi t d t=4 \pi\left[-\frac{\cos \pi t}{\pi}\right]_{t_1}^{t_2}\)

= 4(cosπt_{1}– cosπt_{2})

1. In this case, t_{1} = 0 and t_{2} = 1s

Therefore, Q_{1} = 4(cos0- cosπ)

= 4[1 – (-1)]

= 8C

2. In this case, t_{1} = 1s and t_{2} = 2s

Therefore, Q_{2} = 4(cos_{1}π- cosπ)

= 4(-1- 1)

= -8 C

Here the current I- Ansinnt denotes an alternating current (see chapter ‘Alternating Current7 for details). Its time period is 2 seconds. The above example indicates that in the first half cycle i.e., in the first 1 second, the amount of charge flowing through any cross-section is equal to the charge flowing in the second half cycle i.e., in the next 1 second but in the opposite direction. So, that net charge flowing through any particular cross-section inside a conductor in a total cycle is zero. It is a property of an ac.

**Conventional Direction of Electric Current:**

Of two bodies, the body at a higher potential is called a positively charged body and the body at a lower potential is called a negatively charged body. Similar is the die case for Two points on a conductor.

Now, from the properties of electric potential we know that ‘See Chapter ‘Electric Potential’]

If free positive charges are in a conductor the flow from the highs- to the lower parentis] and

If free negative charges exist in a conductor, the Sow from the lower to the higher potential La, the directions of Sow of positive and negative charges are opposite to each other We take, the direction of flow of free positive charge as the direction of flow of electric current La, conventionally, the direction of flow of current is from higher potential to lower potential

It is to be noted that water flows from a higher level to a lower level. Similarly, heat flows from a higher temperature to a lower temperature. So conventional direction of current from higher potential to lower potential is analogous to the flow of water or flow of heat.

In a metallic conductor current flows due to the movement of free electrons. Since the electrons are negatively charged, they flow from lower potential to higher potential. So this direction is obviously opposite to the conventional direction of current.

**Direct current or dc:** If a current flows continuously in the same direction through a conductor, it is called direct current or dc.

**Alternating current or ac:** if a current flowing through a conductor periodically reverses its direction, it is called an alternating current or ac.

**Source of Electric Current:**

The flow of water and electric current are two similar phenomena. It is easily understood that the flow of water through pipe C will not continue for a long period because the levels of water in vessels A and B will become equal within a short time.

But if the difference of water level is maintained with the help of the pump ‘By sending water continuously from vessel B to vessel A, water will continue to flow through pipe C.

It is to be noted that to operate the pump P energy must be supplied by an external source. This external energy acts as the source of the flow of water in the pipe C.

Similarly to get a continuous flow of currentin the conductor C by maintaining constant potential difference between the bodies A and B, an arrangement similar to the pump P is required. This arrangement continuously sends positive charges from body B to body A.

To do this work the arrangement takes the help of some external source of energy. As a result, a constant potential difference is maintained between the two bodies.

So this arrangement P is the source of continuous flow of current in the conducting wire C. This is called the source of electricity in short.

On observing and considering the similarity between flow of water and electric current some relevant information is are obtained

**1. Electric circuit:** The path ACBPA is a continuous path i.e., there is no break in the path of flow of free charges. This type of continuous path is called an electric circuit.

**2. Closed circuit and open circuit:** By using a stopcock in a pipe through which water flows we can maintain the flow or stop it according to our will. Similarly by using a switch in an electrical circuit, current may be allowed to flow or it may be stopped. If the switch is on, there is no break in the circuit. This is called a closed circuit. Againif the switch is off, the circuit becomes discontinuous. It is called an open circuit. The current does not flow in an open circuit.

**3. Uniformity of electric current:** Obviously the rate of flow of free charges through every point of a closed circuit is the same i.e., current flow uniformly in every part of a closed circuit. It fol]pws an important principle, which states that charges do not accumulate at any point in a conductor carrying a current, In other words, there is no source or sink for electric charges, in a conductor.

**4. Internal circuit:** In the part BPA of the circuit, any form of external energy is converted to electrical energy. This part of the circuit is included in the source of electricity and is called the internal circuit.

**5. External circuit:** In the part ACB of the circuit, electrical energy is converted to any other form of energy; e.g., by lighting an electric lamp, heat energy and light energy are obtained, and from an electrical fan mechanical energy is obtained. This part ACB of the circuit is called an external circuit.

**6. Direction of electric current:** The potential of the body A (VA) is higher than that of the body B ( VB). So in the external circuit i.e., in the part ACB current flows from higher potential to lower potential. But in the source of electricity i.e., in the internal circuit (in the part BPA) current flows from lower potential to higher potential.