Circuits- Series-parallel battery?

Question

There is a battery shown with 3 resistors. Starting from the left

between A and B there is a single resistor with 10 Ohms resistance. Between B and C there are two resistors in parallel with a resistance of 10 ohms each.

The total E= 30V

a. What is the equivalent resistance between points B and C?

b. What is the current in each part of the circuit?

c. What is the potential difference between points A and B? Between B and C? A and C?

d. What is the power dissapated in each resistor? What is the power generated in the battery?

Answer 1

a. Parallel resistance is

1/Rt = 1/R1 + 1/R2 ...+1/Rn

1/Rt = 1/10 + 1/10 = 5 ohms

b. Total resistance is 15 ohms so total current at 30 volts is E=IR

30=15I

I=2 amps

Current from A to B is 2 amps

Current from B to C is 1 amp in each resistor.

c. Potential difference from  A to B

E=IR

E=2 * 10 = 20 volts

Potential difference from  B to C

E=IR

E=2 * 5 = 10 volts

d. Power

P=EI = 20 * 2 =40 watts A to B

P=EI = 10 * 1 = 10 watts in each parallel resistor

P=EI = 30 * 2 = 60 watts generated by the battery

Answer 2

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