To determine the decrease in voltage across the 60 W bulb when a 240 W heater is switched on in parallel, we need to analyze the circuit using Ohm's Law and the principles of parallel circuits. Let's break this down step by step.
Understanding the Circuit Configuration
In a parallel circuit, the voltage across each component remains the same, but the total current drawn from the supply increases. The supply voltage is 120 V, and we have a 60 W bulb and a 240 W heater connected in parallel, with lead wires that have a resistance of 6 ohms.
Calculating the Current Drawn by Each Device
First, we need to calculate the current drawn by both the bulb and the heater:
- For the 60 W bulb: Using the formula P = V × I, we can rearrange it to find the current: I = P / V.
- Substituting the values: I_bulb = 60 W / 120 V = 0.5 A.
- For the 240 W heater: Similarly, we calculate the current for the heater.
- Using the same formula: I_heater = 240 W / 120 V = 2 A.
Total Current and Voltage Drop Calculation
Now, let's find the total current flowing through the lead wires when both devices are on:
- Total Current: I_total = I_bulb + I_heater = 0.5 A + 2 A = 2.5 A.
Next, we need to calculate the voltage drop across the lead wires due to their resistance:
- Voltage Drop: Using Ohm's Law, V_drop = I_total × R.
- Substituting the values: V_drop = 2.5 A × 6 Ω = 15 V.
Finding the New Voltage Across the Bulb
The voltage across the bulb after the heater is switched on can be calculated by subtracting the voltage drop from the supply voltage:
- New Voltage Across Bulb: V_bulb_new = V_supply - V_drop = 120 V - 15 V = 105 V.
Calculating the Decrease in Voltage Across the Bulb
Finally, we can find the decrease in voltage across the bulb:
- Initial Voltage Across Bulb: 120 V.
- Decrease in Voltage: Decrease = Initial Voltage - New Voltage = 120 V - 105 V = 15 V.
However, it seems there might be a misunderstanding in the options provided, as the calculated decrease is 15 V, which does not match any of the given choices. It’s essential to double-check the problem setup or the options provided.
Final Thoughts
In summary, when the 240 W heater is switched on, the voltage across the 60 W bulb decreases significantly due to the increased current draw and the resistance of the lead wires. The calculations show a decrease of 15 V, indicating that the bulb will not operate at its full brightness. If you have any further questions or need clarification on any part of this process, feel free to ask!
