Given Information:
Capacitor 1 = C₁ = 100 μF
Capacitor 2 = C₂ = 300 μF
Voltage rating of capacitor 1 = 25 V
Voltage rating of capacitor 2 = 35 V
Supply voltage = Vs = 100 V
Required Information:
Which capacitor will be damaged = ?
Answer:
Capacitor 1 will get damaged
Explanation:
The given two capacitors are connected in series, the equivalent capacitance will be
[tex]C_{eq} = \frac{C_{1} \cdot C_{2} }{C_{1}+C_{2}}\\\\C_{eq} = \frac{100\cdot 300}{100+300} \\\\C_{eq} = 75 \: \mu F[/tex]
The voltage across the capacitor 1 is
[tex]V_{1} = \frac{C_{eq} }{C_{1} } V_{s} \\\\V_{1} = \frac{75 }{100} 100 \\\\V_{1} = 75 \: volts[/tex]
Since the voltage rating of capacitor 1 is 25 volts, it will get damaged because 75 volts are much greater as compared to its voltage rating.
The voltage across the capacitor 2 is
[tex]V_{2} = \frac{C_{eq} }{C_{2} } V_{s} \\\\V_{2} = \frac{75 }{300} 100\\\\V_{2} = 25 \: volts[/tex]
Since the voltage rating of capacitor 2 is 35 volts, it will not get damaged because 25 volts are less as compared to its voltage rating.
