D.C. Circuit

The closed path followed by direct current (d.c.) is called a d.c. circuit. A d.c. circuit essentially consists of a source of direct voltage (e.g., battery), the conduc-tors used to carry current and the load. Fig. shows a torch bulb (i.e., load) connected to a battery through conducting wires. The direct current starts from the positive terminal of the battery and comes back to the starting point via the load. The direct current follows the closed path ABCDA and hence ABCDA is a d.c. circuit. The load for a d.c. circuit is usually a resistance. In a d.c. circuit, loads (i.e., resistances) may be connected in series or parallel or series-parallel.

Combination of Resistors

Series

Potential difference distributes in the ratio of resistance i.e.

Equivalent resistance of the given combination is given as

If n resistors are arrange in series then the equivalent resistance will be

Note:

The current in each resistor is same.
The sum of the potential difference developed across each resistor is equal to the potential difference across the terminals of the combinationm, i.e. V = V₁ + V₂ + V₃ + …………….
If n identical resistance are connected in series and p.d. across each resistance ]

Parallel

Two or more resistor are said to be connected in parallel if the same potential difference exists across all the resistors.

Current distributes in the reverse ratio of their resistance i.e.

Equivalent resistance of the given combination is

If n resistor are arranged in parallel then the equivalent resistance will be:

Note:

The potential difference across each resistor is same.
Current divides at one junction and adds at another junction.
In n identical resistance are connected in parallel
Using n conductors of equal resistance, the number of possible combinations is 2ⁿ ¹.
If the resistance of n conductors are totally different, then the number of possible combinations will be 2ⁿ.