The figure below is closed circuit with 3 capacitors C1 is 40F,C2 is 20F and C3 is 10F.A voltage of 50V is applied across the circuit.Determine the voltage across each capacitor?

To determine the voltage across each capacitor in the circuit, we can use the formula for capacitors in series:

1/C_total = 1/C1 + 1/C2 + 1/C3

1/C_total = 1/40 + 1/20 + 1/10
1/C_total = 1/40 + 2/40 + 4/40
1/C_total = 7/40

C_total = 40/7

Now we can find the voltage across each capacitor using the formula:

V = Q/C

Where Q is the charge stored in the capacitor.

For C1:
V1 = Q/C1
Q = C1 * V_total
Q = 40/7 * 50
Q = 200/7

V1 = (200/7) / 40
V1 = 5V

For C2:
V2 = Q/C2
Q = C2 * V_total
Q = 20/7 * 50
Q = 100/7

V2 = (100/7) / 20
V2 = 5V

For C3:
V3 = Q/C3
Q = C3 * V_total
Q = 10/7 * 50
Q = 50/7

V3 = (50/7) / 10
V3 = 5V

Therefore, the voltage across each capacitor is 5V.

Step 1: Calculate the total capacitance of the circuit

The capacitors are connected in parallel, so the total capacitance is the sum of the individual capacitances:

```
Ct = C1 + C2 + C3
Ct = 40 F + 20 F + 10 F
Ct = 70 F
```

Step 2: Calculate the charge on each capacitor

The charge on a capacitor is given by:

```
Q = CV
```

where:

- Q is the charge in coulombs
- C is the capacitance in farads
- V is the voltage in volts

Since the voltage across the circuit is 50 V, the charge on each capacitor is:

```
Q = CtV
Q = 70 F - 50 V
Q = 3500 C
```

Step 3: Calculate the voltage across each capacitor

The voltage across each capacitor is given by:

```
V = Q/C
```

Substituting the values of Q and C, we get:

```
V1 = Q/C1 = 3500 C / 40 F = 87.5 V
V2 = Q/C2 = 3500 C / 20 F = 175 V
V3 = Q/C3 = 3500 C / 10 F = 350 V
```

Therefore, the voltage across each capacitor is:

- V1 = 87.5 V
- V2 = 175 V
- V3 = 350 V