Basic Electricity - parellel combination of resistors
1 Answer
When resistors are connected in parallel in an electrical circuit, they share the same two nodes, which means they have the same voltage across them. This is in contrast to resistors connected in series, where the current passing through them is the same.
Here are some key points about resistors in parallel:
Voltage: Resistors in parallel have the same voltage across them. This is because both ends of all the resistors are connected to the same two points in the circuit.
Current: The total current entering a parallel combination of resistors is equal to the sum of the currents through each resistor. Each resistor allows a different amount of current to pass through it based on its resistance value according to Ohm's Law:
=
I=
R
V
, where
I is the current,
V is the voltage, and
R is the resistance.
Equivalent Resistance: The equivalent resistance (
eq
R
eq
) of resistors in parallel is given by the reciprocal of the sum of the reciprocals of individual resistances:
1
eq
=
1
1
+
1
2
+
1
3
+
…
R
eq
1
=
R
1
1
+
R
2
1
+
R
3
1
+…
The equivalent resistance of parallel resistors is always smaller than the smallest individual resistance. If all the resistances are equal, the equivalent resistance is equal to the resistance of a single resistor divided by the number of resistors.
Power: Each resistor in parallel dissipates power based on its resistance and the voltage across it. The total power consumed by the parallel combination is the sum of the power dissipated by each resistor.
When analyzing parallel resistor configurations, it's helpful to remember that resistors with lower resistance values will carry more current, and resistors with higher resistance values will carry less current. This can have practical implications when designing circuits to handle different loads and ensure that each resistor remains within its power rating.
To summarize, when resistors are connected in parallel, they have the same voltage across them but different current flowing through them. The equivalent resistance of parallel resistors is less than the smallest individual resistance.
Here are some key points about resistors in parallel:
Voltage: Resistors in parallel have the same voltage across them. This is because both ends of all the resistors are connected to the same two points in the circuit.
Current: The total current entering a parallel combination of resistors is equal to the sum of the currents through each resistor. Each resistor allows a different amount of current to pass through it based on its resistance value according to Ohm's Law:
=
I=
R
V
, where
I is the current,
V is the voltage, and
R is the resistance.
Equivalent Resistance: The equivalent resistance (
eq
R
eq
) of resistors in parallel is given by the reciprocal of the sum of the reciprocals of individual resistances:
1
eq
=
1
1
+
1
2
+
1
3
+
…
R
eq
1
=
R
1
1
+
R
2
1
+
R
3
1
+…
The equivalent resistance of parallel resistors is always smaller than the smallest individual resistance. If all the resistances are equal, the equivalent resistance is equal to the resistance of a single resistor divided by the number of resistors.
Power: Each resistor in parallel dissipates power based on its resistance and the voltage across it. The total power consumed by the parallel combination is the sum of the power dissipated by each resistor.
When analyzing parallel resistor configurations, it's helpful to remember that resistors with lower resistance values will carry more current, and resistors with higher resistance values will carry less current. This can have practical implications when designing circuits to handle different loads and ensure that each resistor remains within its power rating.
To summarize, when resistors are connected in parallel, they have the same voltage across them but different current flowing through them. The equivalent resistance of parallel resistors is less than the smallest individual resistance.