Answer to Question #226659 in Electric Circuits for samsam

Question

Three resistors of resistance 10Ω, 20Ω, and 15kΩ are connected in parallel across a 20V supply.

a) Determine the currents in each resistor and the total current from the supply

b) If the 20Ω resistor becomes disconnected, recalculate the current as in a). Using the results, discuss why parallel connections are commonly used in electrical connection inside the house.

c) With all three resistors connected, a fourth 5Ω resistor is connected in parallel to the other three resistors. Calculate the current through the four resistors and the total current from the supply

Answer 1

a) The current in each resistor is different because for parallel connection, the voltage is the same across each resistor but the resistance is different.

$$I_1=\frac{V}{R_1}=2\Omega,\\\space\\ I_2=\frac{V}{R_2}=1\Omega,\\\space\\ I_3=\frac{V}{R_3}=0.0013\Omega.$$

the total current:

$$I=I_1+I_2+I_3=3.0013\Omega.$$

b) The currents in the first and third resistor won't change. That is why electric circuits in houses are mainly made with parallel connection of elements: one broken element does not affect other.

c) The current in the last resistor:

$$I_4=\frac{V}{R_4}=4\Omega.\\\space \\ I=I_1+I_2+I_3+I_4=7.0013\Omega.$$