Question

calculate the voltage across c1 in the following circuit if the total voltage is 12 v . assume c1 = 5.0 μf , c2 = 17 μf .

Answer 1

To calculate the voltage across capacitor C1 with capacitors C1 and C2 in series and a total voltage of 12 V, first find the equivalent series capacitance and then use the ratio of the equivalent capacitance to C1's capacitance to find V1, yielding approximately 9.27 V.

Step-by-step explanation:

Calculating the Voltage Across Capacitor C1

To calculate the voltage across capacitor C1 in the given circuit with capacitors C1 and C2, where C1 = 5.0 μF and C2 = 17 μF, and the total voltage is 12 V, we need to determine the equivalent capacitance of the circuit first. Since the capacitors are likely connected in series (as no circuit diagram is provided, we make this assumption for the purpose of the exercise), their equivalent capacitance (Ceq) can be calculated using the formula for series connection:

1. 1/Ceq = 1/C1 + 1/C2
2. Ceq = 1 / (1/5 + 1/17) μF
3. Ceq = 1 / (17+5)/(5*17) μF
4. Ceq = (5*17)/(17+5) μF
5. Ceq = 85/22 μF

Once we have the equivalent capacitance, the voltage across C1 (V1) can be found using the total voltage (Vt) and the ratio of the equivalent capacitance to the capacitance of C1 as follows:

1. V1 = (Ceq / C1) * Vt
2. V1 = (85/22 / 5) * 12 V
3. V1 = (85/110) * 12 V
4. V1 = 0.7727 * 12 V
5. V1 ≈ 9.27 V

This result assumes that the capacitors are connected in series, and the total supply voltage is distributed across the capacitors proportional to their equivalent capacitance