Consider the circuit of three identical batteries and three identical bulbs conn

Question

Consider the circuit of three identical batteries and three identical bulbs connected exactly as shown here. In this problem, assume that each battery is a perfect physics battery supply voltage V and the bulbs are perfect ohmic devices with resistance R.

A friend of yours says, "That middle battery is hooked up backwards! The bulbs won't light if you hook the circuit up like that."

a) Respectfully and thoroughly explain to your friend that the bulbs will indeed light.

In your explanation, use both math and cenceptual understanding. Try using the ski-area analogy to help.

b) Find the voltage drop across each resistor

c) Find the power dissipated by each bulb and the total power dissipated by the circuit.

Explanation / Answer

Part a)

Applying Kirchhoff's voltage rule in the above circuit

V -iR -V -iR + V -iR = 0

Gives V -3iR = 0 => i = V/3R

Since current is flowing in the circuit through each resistor hence bulbs will indeed light.

also here total potential is not zero so bulbs will indeed light.

Part b)

voltage drop across each resistor = iR = V/3

Part b)

power dissipated by each bulb = i2R = (V/3R)2*R = V2/9R

and the total power dissipated by the circuit = 3* i2R = V2/3R

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