3. You have a simple circuit with a light bulb (R = 50 Ω) and a power supply (you can treat it like a battery with 120 V). Unfortunately, a loose screw fell on the circuit and is connected in parallel to the light bulb. You can treat the screw as a resistor with a resistance of 1 Ω.
a. Sketch this circuit
b. What effect does the screw have on the circuit? Focus on the current and voltage.
c. This situation is also known as a “short circuit.” Why is this bad if it happens at home?
a. If the 12ov supply holds up, you have a parallel circuit with a 1 ohm and a 50 ohm resistor in parallel.
b. The current drawn by the lamp:
I = V / R = 120 / 50 = 2.4 Amps.
The current drawn by the 1 ohm resistor:
I = V / R = 120 / I = 120 Amps.
The total current:
I(tot) = 2.4 + 120 = 122.4 Amps.
These calculations were based on the assumption that the 120v supply remained constant This is unlikely
unless the current rating of the power supply is well over 120 Amps. A 1 ohm
resistor connected across a 120v 5 Amp
supply would definitely be a short circuit. But if it is connected across a 120v 100 Amp supply; it would be an overload but not a short circuit.
c. A short circuit can trip a circuit breaker, blow a fuse, or burn the house down.
a. To sketch the circuit, you would draw a power supply (battery) symbol with a positive and negative terminal. Connect the positive terminal of the power supply to one end of the light bulb, and the negative terminal of the power supply to the other end of the light bulb. Next, draw a branch from the positive terminal of the power supply and connect it to one end of the screw. Finally, connect the other end of the screw to the negative terminal of the power supply.
b. The addition of the screw, connected in parallel to the light bulb, creates an alternate pathway for current to flow. In other words, current can now choose to flow through either the light bulb or the screw.
In this situation, the screw acts as an additional resistor in parallel with the light bulb. This means that by Ohm's Law, the overall resistance of the circuit decreases. The total resistance in a parallel circuit is given by the reciprocal of the sum of the reciprocals of the individual resistances. In this case, the reciprocal of the total resistance is equal to the sum of the reciprocals of the light bulb resistance and the screw resistance:
1 / RT = 1 / RL + 1 / RS
where RL is the resistance of the light bulb (50 Ω) and RS is the resistance of the screw (1 Ω).
Calculating the reciprocal of RT:
1 / RT = 1 / 50 Ω + 1 / 1 Ω = 0.02 + 1 = 1.02
Taking the reciprocal, we find that:
RT = 1 / 1.02 ≈ 0.98 Ω
This means that the overall resistance of the circuit is approximately 0.98 Ω, which is significantly lower than the original resistance of just the light bulb (50 Ω).
Due to the lower overall resistance, the addition of the screw causes an increase in the current flowing through the circuit. This is because according to Ohm's Law (V = IR), keeping the voltage constant (120 V in this case), a lower resistance results in a higher current. So, the presence of the screw in parallel with the light bulb causes more current to flow through both the light bulb and the screw.
c. This situation is also known as a "short circuit." It is considered bad if it happens at home because it can lead to dangerous consequences.
In a short circuit, a very low resistance is created, causing an excessive current to flow through the circuit. This can result in overheating, melting of wires, and potentially starting a fire. The increased current can overload the circuit and damage electrical devices or appliances connected to it.
Furthermore, the high current in a short circuit can cause the circuit breaker or fuse to trip, interrupting the flow of electricity. This is a protective measure designed to prevent further damage or hazards.
Hence, it is important to prevent short circuits from occurring by properly insulating and securing electrical connections in our homes.