Four resistors , each of 240ohms are connected in parallel , and the group then joined in series with a heater of 40ohms resistance. Then complete circuit is connected to a 240volts supply . Calculate total resistance in the circuit , the power dissipated in the parallel group and the energy dissipated by the heater in joule per minute
the 4 240Ω resistors have a combined resistance of 60Ω
Add that to the 40Ω in series, and the total is 100Ω
P = E^2/R, so the parallel group dissipates
960W
Now just figure the energy of the heater.
To calculate the total resistance in the circuit, we need to determine the equivalent resistance of the parallel group of resistors and then add it to the resistance of the heater in series.
Step 1: Calculate the equivalent resistance of the parallel group of resistors.
When resistors are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.
1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4
Since all four resistors are of the same value (240 ohms), we can substitute this value into the equation:
1/Req = 1/240 + 1/240 + 1/240 + 1/240
1/Req = 4/240
1/Req = 1/60
Therefore, the equivalent resistance of the parallel group is 60 ohms.
Step 2: Calculate the total resistance in the circuit.
The total resistance (Rt) is the sum of the equivalent resistance of the parallel group and the resistance of the heater in series.
Rt = Req + Rh
Rt = 60 ohms + 40 ohms
Rt = 100 ohms
Step 3: Calculate the power dissipated in the parallel group of resistors.
Power (P) can be calculated using the formula:
P = (V^2) / R
Where V is the voltage (240 volts) and R is the resistance (60 ohms).
P = (240^2) / 60
P = 5760 Watts
Step 4: Calculate the energy dissipated by the heater in joules per minute.
Power (P) is measured in watts. Since we want to know the energy dissipated in joules per minute, we need to convert watts to joules per minute.
1 Watt = 1 Joule per second
Therefore,
1 Watt = 60 Joules per minute
To calculate the energy dissipated by the heater:
Energy = Power × Time
The time unit is in minutes, so we need to multiply the power by 60.
Energy = Power × 60
Energy = 5760 Watts × 60
Energy = 345,600 Joules per minute
In summary,
Total resistance in the circuit is 100 ohms.
Power dissipated in the parallel group of resistors is 5760 Watts.
Energy dissipated by the heater is 345,600 Joules per minute.