Fuse Rating for Parallel Lamps
A student sets up a 6.0 V battery, a switch, a 1.0 A fuse and three identical lamps in parallel. Each lamp is rated 6.0 V, 0.30 A. With the switch closed, all three lamps light normally and the fuse does not blow. The student then adds a fourth identical lamp in parallel, keeping the same 1.0 A fuse. When the switch is closed, the fuse blows immediately. The student says the fuse must be faulty because the battery can deliver up to 2.0 A and each lamp only takes 0.30 A. He proposes replacing the fuse with a 5.0 A fuse so that more lamps can be added. The teacher asks him to calculate the currents, explain the fuse failure, and recommend a safer fuse rating. Assume the battery maintains 6.0 V and the lamps have constant resistance.
1. Calculate the total current with three lamps and with four lamps. Explain why the 1.0 A fuse blows.
Read the worked answer
In a parallel circuit each lamp is connected directly across the 6.0 V supply, so each lamp takes its normal current of 0.30 A.
With three lamps:
I = 3 × 0.30 = 0.90 A
This is below 1.0 A, so the fuse does not blow.
With four lamps:
I = 4 × 0.30 = 1.20 A
This is above the 1.0 A rating, so the fuse wire melts and breaks the circuit. The fuse is not faulty; it is doing its job. The battery's ability to deliver up to 2.0 A is a maximum, not a current that is forced through the circuit. The current is determined by the lamps, and four lamps demand 1.20 A.
2. Recommend a suitable fuse rating and evaluate the proposal to use a 5.0 A fuse.
Read the worked answer
The normal current with four lamps is 1.20 A, so the fuse must be rated above 1.20 A but not far above it. A 2.0 A fuse is suitable: it will carry the normal 1.20 A without melting, but it will blow if the current rises significantly, for example because of a short circuit or too many lamps.
A 5.0 A fuse is not safe for this circuit. It would allow up to 5.0 A to flow before melting, which is much higher than the lamps and connecting wires are designed for. The fuse is there to protect the wiring, not to match the maximum current the battery can supply. Replacing a 1.0 A fuse with a 5.0 A fuse because it keeps blowing removes the protection and could cause overheating or fire.
3. Compare the brightness of the three-lamp and four-lamp arrangements, assuming the battery stays at 6.0 V.
Read the worked answer
Each lamp still has 6.0 V across it in both arrangements, because the lamps are in parallel and the battery voltage is assumed constant. Each lamp therefore carries 0.30 A and dissipates the same power, P = VI = 6.0 × 0.30 = 1.8 W. The brightness of each individual lamp is unchanged when the fourth lamp is added.
The total current increases from 0.90 A to 1.20 A because there is an extra parallel branch. In a real battery with internal resistance, the terminal voltage would fall slightly as the current increases, so the lamps would dim a little. But with the ideal 6.0 V assumption, adding a lamp in parallel does not make the other lamps dimmer; it only increases the total current drawn from the supply.