Question

A circuit contains a 12-volt battery and two 3-ohm bulbs in series.

a. Calculate the total resistance of the circuit.
b. Calculate the current in the circuit.
c. Calculate the power of each bulb.
d. Calculate the power supplied by the battery.

Answer 1

The total resistance of the circuit is 6 ohms. The current in the circuit is 2 amps. The power of each bulb is 24 watts. The power supplied by the battery is 24 watts.

Step-by-step explanation:

a. Calculating the total resistance:

To find the total resistance of a series circuit, you need to add up the individual resistances. In this case, the circuit contains two 3-ohm bulbs in series, so the total resistance is 3 ohms + 3 ohms = 6 ohms.

b. Calculating the current:

To calculate the current in a series circuit, you need to use Ohm's Law: I = V / R, where I is the current, V is the voltage, and R is the resistance. Since the voltage of the battery is 12 volts and the total resistance is 6 ohms, the current is I = 12 V / 6 ohms = 2 amps.

c. Calculating the power of each bulb:

To calculate the power of each bulb, you can use the equation P = I × V, where P is the power, I is the current, and V is the voltage. Since the current flowing through each bulb is the same as the current in the circuit (2 amps) and the voltage across each bulb is the same as the voltage of the battery (12 volts), the power of each bulb is P = 2 A × 12 V = 24 watts.

d. Calculating the power supplied by the battery:

The power supplied by the battery can be calculated using the equation P = I × V, where P is the power, I is the current, and V is the voltage. In this case, the current is 2 amps and the voltage is 12 volts, so the power supplied by the battery is P = 2 A × 12 V = 24 watts.

Answer 2

a). Since the bulbs are in series, their total resistance is the sum of their individual resistances. The total resistance in the series circuit is 6 ohms.

b). The current in the circuit is (voltage between the ends) / (total resistance) .
Current = 12 V / 6 ohms = 2 Amperes.

c). The power dissipated by any component can be expressed in different ways,
and if we're smart, we pick the formula that makes the problem easy for us.

-- Power = (voltage) x (current)
-- Power = (current)² x (resistance)
-- Power = (voltage)² / (resistance)

For this one, I think the middle formula is easiest.

Power = (current)² x (resistance) = (2 A)² x (3 ohms) = 12 watts for each bulb

d). Each bulb dissipates 12 watts,so for both bulbs, the battery has to supply 24 watts.

Check this solution with the first formula for power, above:

-- Power = (voltage) x (current)

Battery power = (battery voltage) x (current) = (12 V) x (2 A) = 24 watts Check. yay!