Solve Resistance Question: Find R of Resistor with 60W Lamp & 120V

• arod2812
Buffet: In summary, the question is asking for the resistance (R) of a resistor in a series circuit with a 60-W lamp and a 120-V source, given that the voltage across the lamp is 35-V. The equation used is P=IV and the attempt at a solution involves finding the current (I) through the lamp and using it to calculate the resistance (R) using the equation R=V/I. However, the calculated resistance of 170 ohms is not the correct answer.
arod2812

Homework Statement

A 60-W lamp is placed in series with a resistor and a 120-V source. If the voltage across the lamp is 35-V, what is the resistance (R) of the resistor?

Homework Equations

I am pretty sure I am using the right equation, but I am not getting the right answer. What am I doing wrong?

The Attempt at a Solution

P=IV --> 60W=I(120V) --> I=-.50 A
R=V/I --> (120V-35V)/.5A = 170 ohms (this is what I calculated but it isn't the right answer)

Voltage across the lamp is 35V, so that in P=VI,V=35 for the lamp.

Current through the lamp = P/V =60/35

A lamp rated as 60W would dissipate 60W when connected directly to the 120V supply -- when you add a resistor in series with it, it no longer dissipates 60W.

- Warren

1. How do I calculate the resistance of a resistor with a 60W lamp and 120V?

To calculate the resistance of a resistor, you can use the formula R = V^2 / P, where R is the resistance in ohms, V is the voltage in volts, and P is the power in watts. In this case, the power is 60W and the voltage is 120V, so the resistance would be (120V)^2 / 60W = 240 ohms.

2. What is the relationship between resistance and power in a circuit?

The relationship between resistance and power in a circuit is described by Ohm's Law, which states that the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance. This means that as resistance increases, power decreases, and vice versa.

3. Can I use a different formula to calculate resistance in this scenario?

Yes, there are other formulas you can use to calculate resistance in a circuit. One alternative is R = V / I, where R is resistance, V is voltage, and I is current. In this case, you would need to know the current flowing through the circuit in order to use this formula.

4. How does the wattage of a lamp affect the resistance of a circuit?

The wattage of a lamp does not directly affect the resistance of a circuit. However, the wattage does affect the amount of power being used in the circuit, which can indirectly impact the resistance. In general, higher wattage lamps will require a lower resistance in order to maintain a safe level of power in the circuit.

5. Is there a limit to the resistance that a circuit can have?

Yes, there is a limit to the resistance that a circuit can have. In theory, the resistance could be infinitely high, but in practical terms, it is limited by the breakdown voltage of the components in the circuit. If the resistance is too high, it may cause the components to fail or the circuit to stop functioning properly.

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