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Bulb Brightness
Bulb Behavior in Electrical Circuits
Relationship Between Bulb Brightness and Power in Electrical Circuits
1. Series Circuits
Circuit Characteristics:
- Same current passes through all bulbs (I constant)
- Total resistance: Rtotal = R1 + R2 + ... + Rn
- Voltage is divided across bulbs
Power
\[ P = I²R \]
Relationship: As resistance increases → power increases → brightness increases
Result: The bulb with higher resistance will be brighter
2. Parallel Circuits
Circuit Characteristics:
- Same voltage across all bulbs (V constant)
- Total resistance: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn
- Current is divided between bulbs
Power
\[ P =\frac { V²}{R}\]
Relationship: As resistance decreases → power increases → brightness increases
Result: The bulb with lower resistance will be brighter
3. Combination Circuits
Circuit Characteristics:
- Mix of series and parallel connections
- Must calculate equivalent resistance for each section
- Current and voltage are distributed according to connections
Circuit Analysis:
1. Break circuit into series and parallel sections
2. Calculate equivalent resistance
3. Use Ohm's Law
\[V = IR \]
Example: If two bulbs are in series with a parallel group:
P for each bulb depends on voltage and current distribution in its branch
Circuit Type Comparison
Type Current Voltage Brightness-Resistance Relationship
Series Equal Different
Directly proportional to resistance
Parallel Different Equal Inversely proportional to resistance
Basic Equations
Ohm's Law
\[V = I × R\]
Electrical Power
\[ P = V × I = I²R =\frac {V²}{R}\]
Where:
V: Voltage (Volts)
I: Current (Amperes)
R: Resistance (Ohms)
P: Power (Watts)
Brightness of a bulb connected to variable resistors
Brightness is power - as power increases, brightness increases when the current through the bulb changes, the voltage changes proportionally with constant bulb resistance. Current is controlled by the variable resistor - increasing resistance decreases current
\[ P = I. V = I^2 . R = \frac {V^2}{ R }\]
Electrical circuit with four identical bulbs
This circuit is a combination of both series and parallel circuits. In series, current is constant while in parallel, current divides. Battery voltage is distributed across loads. In parallel circuits, voltage is equal while brightness depends on power. This simulation shows a combination circuit with a power source, four identical bulbs, and three switches. Open and close the switches to predict voltage across bulbs, current through bulbs, and bulb brightness (related to power dissipated as heat and light). Use checkboxes to show/hide voltages and currents.
Bulb Brightness |
Relationship Between Bulb Brightness and Power in Electrical Circuits
1. Series Circuits
Circuit Characteristics:
- Same current passes through all bulbs (I constant)
- Total resistance: Rtotal = R1 + R2 + ... + Rn
- Voltage is divided across bulbs
Relationship: As resistance increases → power increases → brightness increases
Result: The bulb with higher resistance will be brighter
2. Parallel Circuits
Circuit Characteristics:
- Same voltage across all bulbs (V constant)
- Total resistance: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn
- Current is divided between bulbs
Relationship: As resistance decreases → power increases → brightness increases
Result: The bulb with lower resistance will be brighter
3. Combination Circuits
Circuit Characteristics:
- Mix of series and parallel connections
- Must calculate equivalent resistance for each section
- Current and voltage are distributed according to connections
1. Break circuit into series and parallel sections
2. Calculate equivalent resistance
3. Use Ohm's Law \[V = IR \]
Example: If two bulbs are in series with a parallel group:
P for each bulb depends on voltage and current distribution in its branch
Circuit Type Comparison
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Basic Equations
Ohm's Law \[V = I × R\] Electrical Power \[ P = V × I = I²R =\frac {V²}{R}\]Where:
V: Voltage (Volts)
I: Current (Amperes)
R: Resistance (Ohms)
P: Power (Watts)
Brightness of a bulb connected to variable resistors
Brightness is power - as power increases, brightness increases when the current through the bulb changes, the voltage changes proportionally with constant bulb resistance. Current is controlled by the variable resistor - increasing resistance decreases current \[ P = I. V = I^2 . R = \frac {V^2}{ R }\]
This circuit is a combination of both series and parallel circuits. In series, current is constant while in parallel, current divides. Battery voltage is distributed across loads. In parallel circuits, voltage is equal while brightness depends on power. This simulation shows a combination circuit with a power source, four identical bulbs, and three switches. Open and close the switches to predict voltage across bulbs, current through bulbs, and bulb brightness (related to power dissipated as heat and light). Use checkboxes to show/hide voltages and currents.
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