# Variable Resistance across a Bulb

## Homework Statement

A light bulb and a resistor are connected in series to a variable power supply. A student first connects a voltmeter and an ammeter to measure the current through and the voltage across the bulb, as shown in the left circuit. The student varies the power supply voltage and records the readings on the meters.

The student then places the voltmeter across the resistor as shown in the right circuit, and repeats the experiment. She plots the data for both circuit elements in a single graph, as shown below.

a)Suppose the power supply voltage is now set to +3.0 V. For this power supply voltage, is the absolute value of the voltage across the bulb greater than, less than, or equal to 3.0 V?

b)Use the graph to estimate the current through the bulb when the power supply voltage is +3.0 V.

V=IR

## The Attempt at a Solution

a) The two elements are in series, so I believe the voltage across the bulb would have to be less than 3V

b) I'm having trouble with this since the resistance of the bulb is varying.

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You are absolutely correct.... the resistance of the bulb is changing, it must be a bulb with a metal filament (but that has got nothing to do with this question!!).
The most important thing here is to realise that bulb and resistor are in SERIES. That means that at all times the same CURRENT flows through both.
If you look at the graph and draw horizontal lines through the current values 0.2, 0.3, 0.4 and 0.5 then the voltage on the redline (the resistor) is always greater than the voltage on the curved black line (the bulb)
The most important thing about part (b) of the question is that it asks you to ESTIMATE the current in the circuit.
This usually means that you have to get the answer from a graph and there is not an exact answer..... you have to show that you know what you are doing!!!!
In this question you have 2 components connected in series so I hope you realise that the voltages across each one must add up to the battery voltage.
We are looking for 2 voltages (the red line and the black line) that add up to 3V for a particular current.
Look at a current of 0.2A.... the voltages are (about 0.5 for the black line) and 1 for the red line.... these do NOT add up to 3V
Look at current = 0.3A .....voltage for black line =1.0V and for the red line = 1.5V... ad up to 2.5V
Look at current = 0.4A .... volts for black line = nearly 1.5V and for the red line = 3.0V ....add up to 4.5V !!!!!
Can you make a sensible guess (estimate) of the current that would give a total voltage of 3V

sophiecentaur