The need to combine resistors in series or in parallel occurs so frequently that it warrants special attention. The process of combining the resistors is facilitated by combining two of them at a time.
The two resistors are in series, since the same current i flows in both of them. Applying
Ohm’s law to each of the resistors, we obtain
If we apply KVL to the loop (moving in the clockwise direction), we have
combining, we get
Equivalent Resistance
The Equivalent Resistance of any number of resistors connected in series is the sum of the individual resistance.
To determine the voltage across each resistor...
Notice that the source voltage v is divided among the resistors in direct proportion to their resistances; the larger the resistance, the larger the voltage drop. This is called the principle of voltage division.
| Parallel Resistors and Current Division |
Consider the circuit in Fig. 2.31, where two resistors are connected in parallel and therefore have the same voltage across them. From Ohm’s law,
Applying KCL at node agives the total current i as
Substituting..
where Req is the equivalent resistance of the resistors in parallel:
Equivalent resistance
The Equivalent resistance of two parallel is equal to the product of their resistance divided by their sum.
| Conductance |
It is often more convenient to use conductance rather than resistance when dealing with resistors in parallel.
The equivalent conductance for N resistors in parallel is
Equivalent Conductance
The Equivalent Conductance of resistors connected in parallel is the sum of their individual conductance.
No comments:
Post a Comment