Question

Find the equivalent resistance and the current in each resistor

Answer 1

Equivalence resistance: 3 Ω.

Current:

• 12.0 A in the 1.00 Ω and the 3.00 Ω resistor;
• 4.00 A in the 7.00 Ω and the 5.00 Ω resistor.

Step-by-step explanation:

Equivalent Resistance

The 1.00 Ω resistor and the 3.00 resistor are in series. Add their resistance up to find the equivalent resistance of the upper branch:

`1.00\;\Omega + 3.00 \;\Omega = 4.00\;\Omega`.

Try the same steps for the lower branch. The equivalent resistance of the 7.00 Ω resistor and the 5.00 Ω resistor in series is 12.00 Ω.

The upper and lower branch are in parallel. Take the reciprocal of the resistance of each branch. Add the two reciprocals to each other. The equivalent resistance of the two branches will be the reciprocal of the sum. In other words, the equivalent resistance of resistors
`R_1` and
`R_2` in parallel will be:

`(1)/((1)/(R_1)+(1)/(R_2))`.

For the upper and lower branches in this question, the equivalent resistance will be

`(1)/((1)/(4.00)+(1)/(12.00)) = 3.00\;\Omega`.

Current in each Resistor

The internal resistance of the power supply is 0. As a result, the voltage across the two parallel branches is 48.0 V, the same as the EMF. Since the two branches are connected in parallel, the voltage across both branch will be 48.0 V.

The two resistors in each branch are in series. The current that flows into each branch is the same as the charge that flows out. As a result, the current through the each resistor in a branch will be the same as the current through the entire branch. In other words,

Current in the 1.00 Ω Resistor

= Current in the 3.00 Ω Resistor

= Current in the upper branch

=
`\displaystyle (V)/(R) = (48.0)/(4.00) = 12.0\;\text{A}`.

Try these steps to find the current in the two resistors in the lower branch:

`\displaystyle I_\text{lower}=(V)/(R) = (48.0)/(12.00) = 4.00\;\text{A}`.