How can we determine the number of lamps that a battery can supply in a circuit with specific resistances and voltage values?
To find the number of lamps the battery can supply, calculate the total resistance of the circuit using Ohm's law. Then use the total resistance and the battery voltage to find the current through the circuit. Finally, divide the total current by the current through each lamp to determine the number of lamps the battery can supply.
Calculating Total Resistance:
To determine the number of lamps a battery can supply in a circuit, we first need to calculate the total resistance of the circuit. In this scenario, the internal resistance of the battery is 2.6 ohms, the resistance of each lamp is 200 ohms, and the resistance of conducting wires is 0.40 ohms.
To calculate the total resistance in a parallel connection, we use the formula:
1/R_total = 1/R_1 + 1/R_2 + 1/R_3 + ... + 1/R_n
Substituting the given resistance values, we get:
1/R_total = 1/200 + 1/200 + 1/200 + ... + 1/200
Simplifying the equation, we find:
1/R_total = n/200
R_total = 200/n
By substituting the number of lamps, we find:
R_total = 200/5 = 40 ohms
Calculating Current Through the Circuit:
Next, we need to find the current passing through the circuit using the battery voltage and total resistance calculated.
Using Ohm's law (V = I * R), we rearrange the formula to find the current:
I = V/R
Substitute the values:
I = 130/40 = 3.25 amps
Determining the Number of Lamps:
Finally, to determine the number of lamps the battery can supply, divide the total current by the current through each lamp.
n = I/I_lamp = 3.25/0.65 = 5
Therefore, the battery can supply a maximum of 5 lamps in this circuit setup.