Question

Circuit battery is 24V and R1 is 22 ohms, R2 is ? , R3 is 43 ohms and R4 is 48 ohms. The total supply current is 317ma. Find Vt, Vr1, Vr2, Vr3, Vr4

Answer 1

Assume that $R_1$ is connected in series with $R_2$ and they form one branch, and $R_3$ is in series with $R_4$, which form another branch.

The branches are in parallel. Then the total resistance will be

$$R=\frac{(R_1+R_2)(R_3+R_4)}{R_1+R_2+R_3+R_4}.$$

According to Ohm's law, the supply voltage is total resistance times total current:

$$V=IR.\\ V=I\frac{(R_1+R_2)(R_3+R_4)}{R_1+R_2+R_3+R_4},\\ R_2=429\text{ V}.$$

Calculate the voltage drops across each resistor. As we know, common voltages across resistors [1 in series with 2] and [3 in series with 4] are equal:

$$V=I_1(R_1+R_2)\\ V=I_2(R_3+R_4),\\ I_1=0.0532\text{ A},\\ I_2=0.264\text{ A}.$$

The voltage drops:

$$V_{R_1}=I_1R_1=1.17\text{ V},\\ V_{R_2}=IR_2=22.8\text{ V},\\ V_{R_3}=IR_3=11.4\text{ V},\\ V_{R_4}=IR_4=12.7\text{ V},\\ V_t=V=V_{R_1}+V_{R_2}=V_{R_3}+V_{R_4}=24\text{ V}.$$