27.4:
Combination Of Resistors
Consider a combination circuit consisting of resistors connected to a battery. What will be the current and voltage across each resistor in the circuit?
The known values are the values of the resistors and the battery voltage.The unknowns are the total resistance and total current in the circuit and the current and voltage across each resistor.
The first step is to simplify the two parallel resistors into a single resistor with its equivalent resistance.
Now, the series combination of these two resistors is equivalent to a 5 Ohm resistor.
Using ohm's law, the total current in the circuit is determined to be 4 amperes.
To find the current and voltage across each resistor, revert to the original circuit.
The current in series-connected resistor R1 is the same. So, the I1 equals 4 amperes.
In the parallel combination of two identical resistors R2 and R3, the current is equally divided between them, which is 2 amperes.
Finally, with the known current values and using ohm's law, the voltage drop across each resistor can be determined.
27.4:
Combination Of Resistors
Electrical devices in any circuit can be connected either by series or parallel connections. Additionally, circuits can be connected involving both of these connections, known as combination or complex circuits. As these circuits have complex resistor connections, it is necessary to identify different parts as either series or parallel connections, then the whole combination of series and parallel resistors can be reduced to a single equivalent resistance. With the known equivalent resistance and the total voltage, the total current in the circuit can be determined using ohm's law. This current is distributed to all resistors.
To obtain the current across each resistor, we need to consider the original circuit. If the resistors are connected in series, the current remains the same; if they are connected in parallel, the current divides as per the resistance value. Finally, the voltage drop across each resistor can be determined using Ohm's law with the known current values and the resistors' values.
Complex connections are common when the wire resistance is taken into consideration. In such a scenario, wire resistance is taken in series with other resistances that are in parallel. The resistance of the wires reduces the current value and hence the power delivered to the resistor. If wire resistance is comparatively large, as in the case of a very long wire, this loss can be significant. If a large current is drawn, the IR drop in the wires can also be substantial and may become apparent from the heat generated in the cord.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 10.2; pages 446–449.